I wonder if they didn't make this 3 mana because they want all Ragers to be bad, or whether they found that it was actually too strong at 3 mana while play testing.
This may be playable in a super low curve Token Druid. Perhaps not feasible in Standard, but in Wild there is Living Roots and Mark of the Lotus to enable that archetype.
I play Oaken Summons a lot in Jungle Giants Druid and after quest completion it can pull any minion from your deck. Of course you never know for sure in Hearthstone whether a similar card will work in a similar way, but in the case of Jungle Giants the discounted cards cost 0 while in the deck. I haven't played Oaken Summons plus Embiggen though.
Edit: Made it clear that I'm certain about the Oaken Summons interaction with Jungle Giants; logically Oaken Summons and Embiggen should interact the same but I haven't tested that.
You could play Embiggen, then Guardian Animals, then the second Embiggen. If you have a lot of card draw, it doesn't really matter that you can't use your second copy of Guardian Animals, while if you don't have a lot of card draw, chances are that you either won't draw your second Embiggen or your second Guardian Animals.
If you buff with Embiggen, you increase the cost of the minions in your deck. Unlike variable cost changes on for example giants and Shirvallah, the Tiger, fixed cost changes are applied in-deck. So you'd have to put 4-cost beasts in your deck in order to pull them after casting Embiggen once.
Deck thinning is good, but except in extreme cases (Mysterious Challenger) you don't really want to put cards in your deck that are bad on curve just to be able to pull them. Most of the cheap beasts worth playing in Standard have battlecries and already have rush, so they're missing a lot of value when pulled.
One exception could be Bad Luck Albatross: if you pull one or two of those, your future draws will be significantly better than your opponent's. But ever since it was nerfed, it's not great when played on curve.
If your deck runs Kael'thas Sunstrider, you have a chance to thin your deck for 0 mana, in which case it doesn't matter much if the beasts you pull are skipping their battlecries.
Are you talking about Sap? While annoying to see 9 mana undone, the opponent is using 2 mana and the most versatile card in their deck, so it's not a total loss. Specifically against control, the tempo loss may not be fatal. For Rattlegore, there is always the option to shuffle bombs to turn off their Zephrys off. In theory Bad Luck Albatross allows Demon Hunter to do that too, but since its nerf that's no longer a good card to play on curve.
The point of the comparison was that copying cards from the enemy deck is pretty useful, provided that you don't pay too much for that ability.
If you can copy three cards, you get the best pick from discover plus two others. And since they are discounted to 1, any bad cards won't be clogging your hand. But that is assuming you can copy three cards, which may not be possible in Standard right now.
You are right that it is much harder to use the cards you copied in the same turn with Keymaster. I used Operative mostly to fish for value; copying Death Knights was fun. But having the option to copy something to use immediately can be useful at times.
The original Dr. Boom was run as the top-end in fast decks. So if a 7-mana card helps close out the game, they can run it. But Keymaster is a value generator and that's not what fast decks need at 7 mana.
What you want in control vs control depends on the exact matchup. If you are the player who would win in fatigue, it's up to the other player to put on pressure, in which case more removal can be useful.
In control vs aggro, I agree that you want the likes of Evasive Drakonid and Winged Guardian as your 7-drops: you will out-value them anyway, as long as you can stay alive.
Drakonid Operative was a very good card in its day, so getting cards from your opponent's deck isn't bad in itself. Paying too much mana to get cards from your opponent's deck is bad, but in the case of Operative the big body made the cost worth it, while with Keymaster the tempo gain from getting discounted cards might help. I can see this being useful in Wild, where it can be combined with Naturalize or Coldlight Oracle or Research Project, but I don't remember any card in Standard that does something similar. Of course you'll get one card just from passing the turn, but one might not be enough.
I think that even if you can discount this by only 1 mana it's already good enough. I'm not sure if Priest can make a good deck that can do that consistently, but Paladin has Hand of A'dal so it may fit into decks that don't use Librams as well.
Despicable Dreadlord was a very playable card. The current meta is different: on the one hand there are a lot of low-health minions, on the other hand there is rush now which makes sticking minions on the board harder. But if an opponent runs two rush minions into one of your cards, after it already got its special effect off once, you're probably coming out ahead.
Mage does have Astromancer Solarian as a cheap playable spellpower minion. Of course having two legendaries in your hand at the right time doesn't happen often, but if it's already playable without a spellpower buff, the buff is an upside that can swing games once in a while.
And in Shaman you get spellpower from your totems, so you will be able to get the buff at some point.
In both classes, Ethereal Augmerchant would be an option: when you can't make use of the spellpower, you can still use that as a better-statted Elven Archer.
A Druid healing a big minion with Groundskeeper can allow making a trade and have the minion survive the next turn, so it does have some value there. On turn 4, you won't often get full (or any) value out of the heal, but a yeti with taunt is still not bad. The bigger problem might be that Ramp Druid wants to play Overgrowth on turn 4.
I can see this being played in a Zoolock with Magic Carpet, EVIL Genius and Disciplinarian Gandling. Or perhaps in a deck with Brittlebone Destroyer and Flesh Giant.
I wonder if they didn't make this 3 mana because they want all Ragers to be bad, or whether they found that it was actually too strong at 3 mana while play testing.
...unless you're Warlock.
It comes close to pre-nerf Battlefiend, so definitely good and maybe OP.
This may be playable in a super low curve Token Druid. Perhaps not feasible in Standard, but in Wild there is Living Roots and Mark of the Lotus to enable that archetype.
I play Oaken Summons a lot in Jungle Giants Druid and after quest completion it can pull any minion from your deck. Of course you never know for sure in Hearthstone whether a similar card will work in a similar way, but in the case of Jungle Giants the discounted cards cost 0 while in the deck. I haven't played Oaken Summons plus Embiggen though.
Edit: Made it clear that I'm certain about the Oaken Summons interaction with Jungle Giants; logically Oaken Summons and Embiggen should interact the same but I haven't tested that.
Unless they programmed an order specifically for this card, I think it will be the oldest minion first (like deathrattles).
You can still use one-sided AoE, like Breath of the Infinite and Holy Nova.
You could play Embiggen, then Guardian Animals, then the second Embiggen. If you have a lot of card draw, it doesn't really matter that you can't use your second copy of Guardian Animals, while if you don't have a lot of card draw, chances are that you either won't draw your second Embiggen or your second Guardian Animals.
Pulling Zixor and a Tiger is not bad though, since you'd shuffle the prime into your deck at a time when you have enough mana to summon it when drawn.
Technically they also have Druid of the Claw, but that only becomes a beast after you pick a form, so it cannot be pulled by this spell either.
If you buff with Embiggen, you increase the cost of the minions in your deck. Unlike variable cost changes on for example giants and Shirvallah, the Tiger, fixed cost changes are applied in-deck. So you'd have to put 4-cost beasts in your deck in order to pull them after casting Embiggen once.
Deck thinning is good, but except in extreme cases (Mysterious Challenger) you don't really want to put cards in your deck that are bad on curve just to be able to pull them. Most of the cheap beasts worth playing in Standard have battlecries and already have rush, so they're missing a lot of value when pulled.
One exception could be Bad Luck Albatross: if you pull one or two of those, your future draws will be significantly better than your opponent's. But ever since it was nerfed, it's not great when played on curve.
If your deck runs Kael'thas Sunstrider, you have a chance to thin your deck for 0 mana, in which case it doesn't matter much if the beasts you pull are skipping their battlecries.
Are you talking about Sap? While annoying to see 9 mana undone, the opponent is using 2 mana and the most versatile card in their deck, so it's not a total loss. Specifically against control, the tempo loss may not be fatal. For Rattlegore, there is always the option to shuffle bombs to turn off their Zephrys off. In theory Bad Luck Albatross allows Demon Hunter to do that too, but since its nerf that's no longer a good card to play on curve.
The point of the comparison was that copying cards from the enemy deck is pretty useful, provided that you don't pay too much for that ability.
If you can copy three cards, you get the best pick from discover plus two others. And since they are discounted to 1, any bad cards won't be clogging your hand. But that is assuming you can copy three cards, which may not be possible in Standard right now.
You are right that it is much harder to use the cards you copied in the same turn with Keymaster. I used Operative mostly to fish for value; copying Death Knights was fun. But having the option to copy something to use immediately can be useful at times.
How is this bad with Pit Commander? Sure, you'll have to wait another turn for its ability to trigger, but you get a free 10/10.
This card got nerfed so fast, we didn't even see the original.
The original Dr. Boom was run as the top-end in fast decks. So if a 7-mana card helps close out the game, they can run it. But Keymaster is a value generator and that's not what fast decks need at 7 mana.
What you want in control vs control depends on the exact matchup. If you are the player who would win in fatigue, it's up to the other player to put on pressure, in which case more removal can be useful.
In control vs aggro, I agree that you want the likes of Evasive Drakonid and Winged Guardian as your 7-drops: you will out-value them anyway, as long as you can stay alive.
Drakonid Operative was a very good card in its day, so getting cards from your opponent's deck isn't bad in itself. Paying too much mana to get cards from your opponent's deck is bad, but in the case of Operative the big body made the cost worth it, while with Keymaster the tempo gain from getting discounted cards might help. I can see this being useful in Wild, where it can be combined with Naturalize or Coldlight Oracle or Research Project, but I don't remember any card in Standard that does something similar. Of course you'll get one card just from passing the turn, but one might not be enough.
I think that even if you can discount this by only 1 mana it's already good enough. I'm not sure if Priest can make a good deck that can do that consistently, but Paladin has Hand of A'dal so it may fit into decks that don't use Librams as well.
Despicable Dreadlord was a very playable card. The current meta is different: on the one hand there are a lot of low-health minions, on the other hand there is rush now which makes sticking minions on the board harder. But if an opponent runs two rush minions into one of your cards, after it already got its special effect off once, you're probably coming out ahead.
Mage does have Astromancer Solarian as a cheap playable spellpower minion. Of course having two legendaries in your hand at the right time doesn't happen often, but if it's already playable without a spellpower buff, the buff is an upside that can swing games once in a while.
And in Shaman you get spellpower from your totems, so you will be able to get the buff at some point.
In both classes, Ethereal Augmerchant would be an option: when you can't make use of the spellpower, you can still use that as a better-statted Elven Archer.
A Druid healing a big minion with Groundskeeper can allow making a trade and have the minion survive the next turn, so it does have some value there. On turn 4, you won't often get full (or any) value out of the heal, but a yeti with taunt is still not bad. The bigger problem might be that Ramp Druid wants to play Overgrowth on turn 4.