You can use polling or sockets when the browser is open; the problem is showing those notifications on the phone's lock screen or when you're in another app.
Sometimes I wonder if Apple wouldn't support web apps at all if they could get away with it. A fully functioning PWA could essentially sidestep the app store for a huge class of applications. The incentives really just aren't aligned.
I was under the impression that under memory pressure all of the tabs in every mobile browser (Firefox/Safari/Edge) I have ever used is unloaded by iOS.
