While I get the utility of push notifications and part of me likes the idea, it will get abused in the same way it was on desktop where every second website asks for permission to send you notifications or install a PWA to be able to do so.
I suspect Apple has internally discussed it and concluded that it would too likely be abused and result in a poor user experience.
Also, Apple deliberately does not like background connections for battery saving reasons which is why everyone is required to use their push service, meaning iOS maintains a single energy efficient connection instead of each app maintaining their own TCP connection which may have no regard for energy efficiency.
I acknowledge it's possible that they don't want to remove reasons for people to rather make native apps, but given the other reasons, it would not be my first guess.