Sometimes, sure. Sometimes not, though. I have a PWA for studying kanji that very much benefits from the increased real estate and more focused feel.
I like having that choice.
You aren't required to install PWAs and can generally keep using the site that created the PWA just fine. PWAs are most often a courtesy for mobile users, not a requirement. Don't need or want that courtesy, don't take it. That you spent time to post here without understanding that is some kind of indictment.