What is state restoration? All I want is to go back to where I was, a normal website does that ( e.g. HN). Integration with what? I
literally just wanna browse twitter, like, retweet, and occasionally compose one. Push notifications, they work on every system except iOS. Better UX is using URLs that I can open and share. Better accessibility is HTML that blind users can use. Native apps track you much, much more than websites and can't be uBlocked. Permission model is as good as native, if not better because users blindly give native apps all permissions (see Instagram).
You haven't made a single point, on the contrary, web wins on ALL of them.
The one single point you can make but you didn't, is that native apps often (but not always) feel smoother or more responsive. Which shouldn't be an issue on browsing static content.