Apple is clearly and deliberately using its influence to limit what a web app can do, in many cases to protect users against features that are poorly designed and harmful to privacy.
[0] https://developer.apple.com/notifications/safari-push-notifi...
As to why not mobile Safari, perhaps Apple doesn’t want to be tied to limitations of the design?
Apple’s push notifications on mobile have evolved significantly over time.
Just because they could do something, doesn’t mean it is a good design.
Not so with websites. The bar for including new functionality in browsers is way higher than it is for native apis because there is no way to police abuse.