1. There are times I want to make sure an app is not running (think zoom/hangouts with video access), or a work app that records location
2. The single best way to fix a problem, any problem, is still 'turn it off and back on again'.
I don't want to kill the current activity and hope that the background jobs stop at some point in the nearish future with absolutely no feedback or insight. I want "killall <root app process>" then give the app 5ish seconds to cleanup and if it's still around "killall -9 <root app process>".
Too many apps abusing resources and affecting UI speed is a separate issue, and mobile OS's developed a lot of techniques and technologies to allow apps to work in the background without bothering the user, and without overloading the device's resources. It's a nice set of systems, really, and I would be happy if desktops worked the same way. Nobody would be taking force quit away from me, even if such a system were to be implemented.
Funny, because I think the exact opposite. "Hide" means, "stop showing it for now, but keep it around". "Quit" means, "I'm done with you and I expect you to not be doing any work until I start you again". It's a very significant usability difference.
> On mobile it doesn't happen, and we can thank Android for that
To this day I consider it to be the worst, most dumb idea Android ever had. I hate it. It's the reason I hated my first smartphone. It's the reason why, from the second phone on, I only ever buy top-of-the-line most overpriced flagships available - I have to overprovision resources to ensure the phone works smoothly, because there are countless of background processes doing god knows what, that cannot be killed and prevented from restarting.
I know best when I'm done with an app. I want to be able to kill it, and all its background processes, and I want them to stay dead until I change my mind. If I were designing a mobile OS, I'd make the distinction between "hide" and "quit" as clear as day, and make it an app store policy violation for an app to execute anything in the background after being "quitted" by the user (polling for notifications would be handled by the system).