That sounds pretty reasonable to me. But that still doesn't excuse Apple not implementing it. Apple doesn't implement features like this because they want to maintain app store sales. They do this for them, not their customers.
From observing non-geeks use the "feature", I think that's the right call regardless. It needs to go back to the drawing board, or be scrapped. In general, anything that expands the reach & capabilities of websites should be treated with a ton of suspicion, as a likely vulnerability vector (leaking tracking info; social engineering/phishing vector; straight-up exploitable bugs) or simply a net-negative annoyance for most users.
If Apple thinks push notifications are annoying, why does iOS have them? Again, Apple is protecting their walled garden. That's all this is. There really is no other good faith argument for this.
Web notifications are not comparable to app push.