> the only competitive advantage for apps is push notifications
Don't know about that. What about UX? It's pretty well accepted now that the native controls in apps provide a much less frustrating UX than all but the most meticulously designed web apps, which is a very low percentage right at the top. That's just talking about controls, that's not even to mention the clunkiness of the browser itself (address bar popping up over content, popups offering to remember passwords, all that kind of stuff that detracts from your tailored experience) and to an extent the navigation model (typing in a url rather than tapping an icon for instantaneous checking of a service). Simple stuff like this really matters to the majority of people.
For technically-minded people, we're not as distracted or put off by this 'minor' stuff because we understand the trade offs, reasons for it, depth of it and even how to work around it. Most people don't, they just (probably rightly based on evidence) trust apps to deliver a better and more tailored UX and that's it, that's what they like and want more of.
Don't get me wrong, I love the web, for probably much the same reasons you do. One advantage it definitely has is the ability to avoid downloading apps in the first place. But its competitive disadvantages vs native apps go way beyond push notifications. There's are a lot of things so deeply baked in to the web and browsers that apps do so much better that it will take (software) generations to 'fix', if at all.
Unfortunately for the web, as seen in the last five years or so, these are disadvantages that really, really matter to the majority of people who actually use services. Much more so than the higher level, arguably 'more important' things like security, privacy, storage space, etc that us techies tend to prioritise.