Well, for one, convoke/improvise style cards, or anything with additional/alternate costs, get weird rules-wise if you generally pay costs before casting. Since now you’d be doing part of the cost up front, and part while casting (since you can’t do them before casting, they’re usually illegal game operations without the card instructing it happens). It wouldn’t be a deal-beaker, but it would probably make alternative costs less intuitive than they currently are. Plus, I suspect new players would have to get constantly corrected about playing cards before tapping their mana, which feels pedantic and doesn’t add much except annoyance.
And if you mean making mana generation instant speed, with priority timing, that’s a whole other can of worms, with terrifying implications.