It's kind of funny as a web developer because for the longest time Apple seemed to be the one pushing the mobile web forward but now that web apps are reaching for feature parity with native, Apple's initial momentum seems to be ancient history.
It seems Apple still thinks of the mobile web as a content delivery platform rather than an application platform. Their proprietary additions (mostly CSS) largely focused on making things prettier, their rationale for opting out of standard features (e.g. autoplay) often only work under the assumption that the only use for those features would be in the context of traditional content pages.
You want an app? Develop for our walled garden we tightly control to offer our users the best possible experience. If you want it on the web, stick to creating content our users can consume in Mobile Safari, our app for reading websites.
I'm sure there are a number of legitimate uses but as of now, every craptastic "news" website I visit now wants to pester the hell out of me with notifications when they post new clickbait.
I'd be OK with a small icon in the address bar to indicate push notifications are available on a site but even one pop up asking for permission is too many.