If Apple allows you to install alternative app stores, I assume that means they allow you to "side load" apps. If that's the case, Apple can't really ban you from installing anything.
They could, of course, ban third-party stores from their own app distribution platforms. Otherwise, I imagine not, in the same way that most other general purpose operating systems cannot "ban" things like that. I suppose they could require all apps to be signed and subject to remote signature verification before the OS lets you install them.
This sort of banning is the very thing Epic appears to be trying to prevent. I would guess their legal endgame is to forbid anyone but government agencies impending a store for any reason. Once this is in place there will be no legal way prevent Apple from securing devices from bad actors in the store space.
Edit: In this scenario I am guessing it will not be Apple, but the government who will need to step in and sell store licenses to prevent illegal content... so yay for bribed big government over authoritarian Apple.
