I do care unfortunately... when I switch from a game to Safari to look up tips on how to get better at the game, that game is often force-closed by iOS and I just lost all my progress. If I'm playing a game and I get a text message and switch to Slack to copy a message into iMessage then back to the game, the game has restarted. If I switch from Safari to the camera app to find a picture then back to Safari, I'll find Safari reloading the page, losing my progress on the web form I was filling out. Actually that last point is why I don't use PWAs and prefer the app, because a PWA will almost always handle being closed worse than an app will.

Most apps handle these things gracefully and it's no problem, but when it's a problem it's a real problem.