It's a feature, (unless I'm mistaking the intent of the question slightly.) tl;dr: Burn is too common/frequent an action to actually shuffle on, so charred cards are inserted randomly instead. True shuffling is an interesting/desirable enough ability to stand on its own, maybe even under a different name?!

What actually happens when you burn is the charred card is INSERTED randomly into the deck, preserving the order of the cards. You may still want to burn prior to Divining though, since there's nothing preventing that random insert point from being the very top of the deck!

Divination as a deck ordering ability is intended to give you a certain amount of information about what's coming, and given the way it places other cards on the bottom of your deck, knowing that the things you DON'T choose are likely to be out of reach is a sort of predictive strength that might not be super obvious up front. It's supposed to help you dig through your deck to find Mythics or cards you need, so if we shuffled every time you burned that would undermine a lot of the advantage Divination offers.

It's not just burn, there's other places like Shopworn Bull and The Recursionist that would be worse if they actually reordered your whole deck. Ideally there'd be a cool word for "randomly insert" that everyone knows, (and didn't sound vaguely R-rated) but the word "shuffle" is laden with RNG context that's extremely useful at a glance, even if physical cards could never use this mechanic without a neutral third party. If necessary, you might see a clarifying tooltip creep in about it, but we're trying to use those sparingly.

At the end of the day, the RNG "at the heart of the cards" is a huge part of what makes CCGs tick, but humans are pattern recognition/sorting beasts so we love finding ways to subvert chaos. Burn, Divination, and the random insert formulation of shuffle are all designed to help you thwart lady luck, but hopefully not TOO much.