Closing apps on iOS unless they are using location services in the background (which you can disable) doesn’t save anything in terms of battery life or processor usage most of the time.
Sometimes I find I do need to close an app to “reboot” it. But yes. It’s actually amusing to me to watch people compulsively close their background apps. I used to try to explain why it wasn’t important but I don’t think anyone ever accepted the advice.
My wife is one of these people. I tried to talk her out of it and tell her it actually makes her phone run slower, not faster, but, as typical, she'll listen patiently to what I tell her and then go on doing her own thing anyway, so I eventually gave up.
I’ve seen this brought up in several threads online. I really don’t care about that. The app switcher is not a task manager as you say. The reason I compulsively close apps is the same reason I keep my chrome tabs small. It’s a pain to find the one I want if I don’t