This is something I feel quite strongly about, and I too favour PWAs. I think native apps have their place for now, as a few key APIs are not fully exposed via browsers yet, but the API landscape continues to improve. Apple has even started dev on service workers for Safari, and their IndexedDB implementation is not as buggy as it used to be.
If I'm honest, apps never really made sense to me; they seem to be part of an intrinsically closed eco-system, which feels completely at odds with the initial premise of the internet, and dare I say, computing in general. If you have an Apple product, you must go to the App Store, if you have an Android product, then it's the Play Store etc. The feeling of openness that I became accustomed to (probably from a time before "apps") seems to have taken a step backward with mobile apps, and replaced with an endless need for vendor lock in. It's great for business, but as a user, it feels really restrictive. As a developer, it's not great either.
I believe that as browsers become more standardised (i.e. you don't need rubbish like if(IS_IOS) { ... } else { ... } in your JavaScript), and they start to expose more and more functionality via well-defined APIs, developers will favour the browser as a deployment platform, simply because it'll be more ubuquitous, will be easier to deploy and manage, and will have a lower barrier to entry. Till then, native apps will maintain their position, as they will be the more polished product.
A personal anecdote: I gave my latest app (a PWA - https://usebx.com) to a few small business owners in my home town to use for free. I pointed them to the website, and the first question they asked me was "why can't I find it on the app/play store?". I told them that they needn't go to the app store - just add the webpage to your homescreen, and you're good to go! They much preferred that method, as compared to "faffing around on t'app store" (imagine that said in a Yorkshire accent)! They even loved the app, and as far as I'm aware, found it on par with a native app. My point is, even the fairly long winded process of searching the app store to find an app, then waiting for it to install, was the first thing that came to mind for these non-techy guys. Once they knew about "Add to homescreen", they liked it. I think much of the transition to PWAs will be like this - people struggling free from their habitual need to use vendor specific app stores and eventually embracing the simpler, more open, web-based app paradigm.