People don't switch between ten just-installed apps in under a minute. They do that all the time on the Web. There's more focus on what you're doing when you open an app for the first time, and installing the app in the first place is a strong signal that you're open to entertaining requests to expand permissions, like to receive push notifications. Browsing to a website is something people do on a whim while barely paying attention, which they don't consider any kind of commitment at all, and they're used to sites going away entirely when they close the tab, not sticking around because they clicked "allow" on a dialog that they don't even remember because the action didn't rise to the level of conscious thought, since the web bombards them with "allow/deny" boxes all day long, where "allow" is just the thing that consistently makes the dialog go away the fastest so they can get on with looking at the site.

Web notifications are not comparable to app push.