The fact that Apple has refused to deliver that only proves the point. If they did, many apps wouldn’t be forced to be in the App Store. It’s certainly possible, as iirc, it works on Android for years now.
Incredibly annoying that apple does not support this, while also trying to crack down on apps that is considered to just be a wrapped web-application. (In which case they want you to make a proper web app instead). Even using notifications is not considered enough of a reason to get an app they feel is just a wrapper approved.