Web Push is probably the worst feature ever introduced to the web. I see way too many spammy notififications on PC's of my non-technical friends and parents. Glad that Apple has decided to only allow Web Push for websites added to the home screen.
I don't get why apple does not take a similiar path on mac. Some websites are really apps for me (stuff like overleaf). I would gladly add them as apps and use this to unlock all those advanced functionality. But so far, at least on safari for mac, all those web-push websites are mostly spam. I only have a few where it is useful but I use them, again, like normal apps, and would be fine of adding them to my library.
Nobody uses the mac app-store anyway, so why bother? Why not do it?
Sounds like this is the motivation Apple needs to bring their notification-handling into the next century. I'd love for Apple to give me a way to disable "Try the New Safari!" notifications without opening my terminal.