I read somewhere that it was a compliance requirement for some consoles. The player has to be able to interact with the game after X seconds or something, and that screen gives you a chance to push a button before seeing more cutscenes or something.

I wouldn’t be surprised if that was a requirement for older systems that got carried over because tradition. Like, an arcade game wouldn’t go to the next screen just because you put a quarter in it, it waits until you hit a ready button to confirm you’re ready to play the game.