A few years back we had this same discussion orbiting around Service Workers. Here's a post from 2017 where the top comment argues that what's holding back the web is the lack of Service Workers in Safari: https://news.ycombinator.com/item?id=14489577
Apple shipped Service Workers in WebKit in 2021. Are web apps much better now than in 2017? Frankly it seems about the same. The best web apps are still exercises in minimalism like Wordle, which don't need Service Workers or Web Push.