I'll do you one further. If buy a game on Steam, I should be able to play it on PlayStation as well.

It's the exact same product - the perceived difference is a mirage. Digital media is the only product that works this way, and it's stupid.

Platforms and stores would have to, I don't know, actually compete then. Who offers the better experience? The better price? The better device? Not "You bought your shit here, so you're stuck. Sorry"

Platform holders should take a cut of anything sold on their platform, but it's because a user chose to buy it from them because they offer a better service, not because it's the only way they can use it.

My reservations about DRM aside, you can still achieve this without dropping DRM. It would have copy protection still.