I want to start by saying I don't mind Demon Hunter at the moment. Its power is fine now that Twin Slice and Blade Dance are gone, so I don't harbour any of the hate I had for the class that I did throughout the Year of the Phoenix.
Nevertheless, I still keep wondering why the class needs to exist, especially from an archetype/mechanics viewpoint. I had hoped that within a year it would be given something that makes it feel truly distinct, but as it stands everything it does is just a slight twist on what other classes could do if they were given the tools, if they don't already do basically the same thing. Let's break down DH's archetypes and mechanics to see what I mean:
Hero attacks
Even at the time DH appeared, multiple classes had direct synergy for the hero attacking: warrior had Hack the System, Armored Goon and Galakrond, while druid had Secure the Deck and Gonk, the Raptor had only just rotated out.
It wasn't long before rogue and warrior were given a hefty weapon package in Scholomance, and in DMF shaman joined in with their Enhancement cards. Come Barrens, and rogue has massive weapons that look and feel a lot like DH's attack buffs.
Even without all the fancy stuff, rogue's hero power has been silently begging for cards that synergise with your hero attacking since 2014. Blizzard just never made the cards. It's not a class identity thing either, because most of DH's weapon attack synergy cards would look perfectly sensible in rogue.
Big demons
Warlock...
OK, so you could argue that warlock's class identity prohibits it from getting the burst damage that many of DH's big demons do. Fine, but they don't really need to be demons. You could make exactly the same cards with the beast tribe instead and hand them to hunter. Or maybe make them mechs, or elementals, or dragons etc. Its not difficult to find another appropriate class for the effect if you just switch out the tribe.
Token decks
Surprisingly not druid, because druid's token decks always use mass board buffs and minions buffs are one of the few things DH can't do.
However, what other class has token decks but (almost) no board buffs? Hunter! We can ignore the fact Unseal the Vault buffs the whole board because you usually only press that button once so it's really just 1 big bit of burst damage. What we can't ignore is that Swarm of Locusts is literally just a slightly bigger Command the Illidari, or that they shared token synergy cards in Scholomance.
Tempo deathrattles
The Barrens deathrattle cards could easily have been given to rogue or hunter, and no one would have been shocked. We would all have just gone "Ooh, deathrattle rogue/hunter has a new look."
Lifesteal burst/OTK
OK, so here I admit the other classes with lots of lifesteal would be very weird with Il'gynoth, since all of paladin, priest and warlock are awful at burst damage (at least in Standard). That said, Il'gynoth really just makes an OTK deck, and to be honest it doesn't matter much that the lifesteal keyword is involved. It still follows the process of: stay alive; draw the deck; play ~5 cards and win.
Basically what I'm saying here is that we didn't need DH for another OTK archetype to exist. It could have just been re-branded to fit the theme of another class and the world would turn much the same.
Soul fragments
Warlock... (I don't even need to add anything this time.)
Outcast
Finally, something truly unique to DH! It has one teeny tiny problem though, and is the main reason big demon DH never took off and bonkers cards like Coilfang Warlord are never played: outcast strongly disincentivises playing anything expensive. The end result that outcast isn't a DH mechanic so much as it is an aggro DH mechanic. The trouble is, when the strongest staple cards have outcast (as they would be because the very point of outcast cards is that they are powerful when the condition is met), all DH decks are going to want to use them, rendering entire supported archetypes worthless.
Outcast would be so much better as a mechanic used infrequently to support aggro decks without being central to the class. At that point it could easily be slipped into one of the other classes as their flavour for a year or so. So rather ironically, I think the one thing that truly does set DH apart would be better off as something that didn't.
Concluding remarks
Sadly, the most I can say to justify DH's existence at this point is that at least it meant the other classes could be pushed in other directions. They often went in roughly the same direction anyway, but I suppose that's not DH's fault.
I'm not optimistic about the class' ability to diversify this year while it is still dominated by the staples and design choices from the Year of the Phoenix, but maybe next year the rotation will herald a new era in which HS has 10 meaningfully different classes.