> LoL on the other hand has about 500 champions (give or take)

LoL has 141 champions. Still significantly higher than Dota's 116.

A common note I hear when people discuss open AI playing dota is that it uses pre-made matchups, which reduces the number of matchups considerably.

Would it be that difficult to have the AI play the picking stage? Compared to the complexity of the decisions you have to make during the game, the picks are straightforward - especially if you have performance data on matchups.

The number of practice games the AI would have to play to learn to handle all the heroes goes up drastically, but that's only a matter of time.