Apple will never give in and implement webpush on mobile safari because that would affect their precious app store. How will they extort developers then? That's also the reason mobile safari is so limited in other features.
Apple changes their mind fairly often, so I wouldn't say never. And in general, predictions based on incentives are often good bets but they are less reliable than many people pretend.
Is it possible that they haven't figured out how to sandbox the little bit of code that handles the notification from the rest of the webpage? Maybe this is solved already by the webpush standard but some websites are a ridiculously overcomplicated hot mess of javascript ads which make my phone heat up, I don't want them waking up my phone all the time and draining the battery.