I could probably make this game myself if it weren't for "Skyrim level" graphics and animations. I can't do animations, models, texturing, etc. for shit, but I could program an online version that implements these mechanics I think.

I've actually thought about this before, and the biggest problem for a game like this (besides getting the necessary trademarks and so on) is how exactly the magic system would work.

There was never any suggestion in the books that "amount of magic" was a significant issue for wizards and witches in most cases. They could just fling spells all day, so long as they weren't trying to cast spells that were insanely overpowered.

If you knew how to do the spell, you could just keep doing it more or less.

Which is perfect for a story where you have a narrative, but crap for a game.

So what would the mechanic be for magic? Mana points or something like that? How do you scale the cost of spells correctly?

Also, how do you make every spell interact correctly with objects in the world? If you learned the Levitation Charm, it would either be useless or the game would have to support that charm for most objects in the world. That goes for a LOT of spells, like summoning and banishing.

How do you handle conjuring? What about transfiguration? How do you implement animagi without it feeling like it's a set of dice with too few options?

The mechanics of making this sort of game are the biggest problem IMO, and why it hasn't been done yet. The game engine itself would be a massive undertaking.

Otherwise you end up with something like the Lego Harry Potter games, where the magic was basically an afterthought.