What's the point of Class Identity when everyone has access to some kind of Discover anything?

Just like others said Discover almost exclusively gives you neutral or cards from your class. One exception are for example the three tri-class Discover cards from Gadgetzan. 99% of Discover cards just pull from neutral or your class though. So I’m not sure what exactly you mean there.

And to be honest I would actually enjoy more stuff like the mixing of different classes. For example Witch’s Cauldron is one of my favorite cards. But of course I understand that some people like you don’t enjoy it that much for various reasons.

The best would be they make all sorts of cool cards and then give people a way to play how they want. For example if you don’t like Discover and every class should stick to their thing you make such a rule set. For even crazier Discover/RNG or mixing classes or who knows what it’s a different rule set. And then everyone looks for the “game table” they want to play on: