Not having web push is a feature. They're the 3rd party toolbar or BonziBuddy of the modern web—often enabled, but rarely wanted—however nice an idea they were in theory.
It's a pure loss for non-geek users. It should be disabled—no dialog allowed, even—by default, if the feature's gonna exist. That hitting "allow" on a pane that pops up on a site—something users are conditioned to do without thinking by all kinds of shitty but extremely common web patterns—affects something outside the current site's browser window is unexpected and unwanted by normal users. Cases where it's easy for sites to affect the behavior of a machine, or of the browser, outside the current session on that site, have historically been a big problem for non-geeks, and this is no exception.
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.
I think if Apple really really wanted to implement it if not for the risk to app sales, they'd have it on desktop Safari, at least. As it is, I just think they don't want to implement it, App Store or no.
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.
You must feel that way about push notifications from apps too then? You seem strongly against push. If you only dislike push on websites, why?
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.
Firefox lets me simply deny a web page the ability to send a notification when it attempts to do so, allowing me to only let the apps I want do so, while not bothering me about the majority of web sites that don't use it.
I'd love some data on what percentage of web-push notifications going out are to users who want them, versus to users who didn't realize browsers had added a feature to let websites shit up their desktop, and, like most folks, just click "allow" on everything that pops up on a site (as there's rarely any reason, for normal people, not to) and don't know why or how some site they visited once is sending them stuff.
My experience from my immediate friends and family support circle is "0%" and "100%", respectively, but I'd be open to data showing that the first number is slightly higher than 0%. The "UX" for this feature for normal users is, as far as I can tell, exactly like the bad old days when people'd accidentally install 3rd party "search bars", then not know how to get rid of them.
Historically, browsers have worked to keep web sites from doing things that affect the machine outside that site's browser pane, that normal users don't want or expect them to be able to do.