It looks like the browser crashes on every screen change on Safari 15 on macOS...
It’s been a while since I’ve seen a documentation site with a loader that goes multiple seconds.
Personally I'm still not a fan of PWA. I don't see what they give me as a user, other than a worse experience than a native application would have.
Installs aren’t really an issue, and less so if you like the app store. I can see the point about wall gardens, but you can still just install non-app store programs on all operating systems. Regarding the 30% I not convienced that saving are directly passed on to the end users.
Edit: It just occurred to me that you might be think about software on phones. I don’t exactly care about mobile, but yes, then your argument makes more sense.
The ServiceWorker API has been supported by iOS Safari for years: https://caniuse.com/mdn-api_serviceworker. When people complain about lack of PWA support on iOS Safari, usually the #1 complaint is lack of Web Push: https://caniuse.com/push-api.
In this specific case, the site is working fine on iOS Safari 14, and Safari 15 TP on macOS Big Sur. I'm not sure if there are problems specific to Safari 15 on not-yet-released iOS 15 or macOS Monterey, I don't have an installation of either.
Good, web push is horrible and 99.9% of use cases are malicious. Take a look at your grandma's Android phone and she probably has 12 Chrome notifications saying she won a free iPad because she went on a site that asked to send notifications, and users are so used to user-hostile UX's that force you to agree to everything to use the site, they just hit "allow" so they can get to the content.
I'm not surprised Apple doesn't want that on the iPhone.