Same thing with other systems. Sony doesn't want their games to run on Xbox, and MS doesn't want theirs to run on Playstation. Why? Because then you wouldn't buy their consoles and they wouldn't get the money from licensing and cuts from their digital stores (you'd be free to choose, if your Xbox broke you could get a Playstation and keep going, breaking their revenue modeL). MS does want games to run on Windows along with their consoles because it keeps developers committing to MS's platform because it's sufficiently hard to migrate to the other consoles or OSes.
Gamers can't stop pre-paying for games which launch with tons of bugs or paying for micro-transactions which incentivize abusive game design. I am highly skeptical that even 0.1% of buyers would not play a game they otherwise wanted because it didn't allow some way to recognize your items from another game.