The constant nagging to "download the app" is worse. Notifications can be left off, for a website or an app - this constant install-app-nagging is unavoidable now.

It absolutely IS possible to add the feature, as opt-in like with app permissions, and e.g. with some user-initiated event like audio already does.

The REAL motivation here is money, forcing users to use the appstore, instead of the web which is an open protocol.