http://pwa.rocks have some pretty nice looking examples, and to most users, they wouldn't have a clue if it was native or not if they didn't see the Chrome Browser. But the add to home screen is the true killer app feature here, now your native apps are competing with Chrome Browser apps which is good enough for most use cases.
Just clicking through the samples at pwa.rocks - a good portion of these are demos/prototypes. Some are just well designed responsive websites that aren't much else than a brochure/ecommerce sites. Sure, it's not hard to format content for mobile and make it look nice. There's a couple of good ones on this list, but for the most part I wouldn't put this list against a list of top ten well designed native apps. They're just not comparable.
That said, I'm not arguing against building out nice mobile responsive sites (and this is something that I think gets forgotten way too much with "rich interface" single-page app designs that are all the craze on desktop). I'm a strong believer that every site should be written with mobile in mind first unless there are strong use cases to argue against it. Don't ever force your users to install an app to consume your product unless the product itself is the app.
Yes, you, as a developer, can enjoy some major shortcuts in your development workflow to get an app like experience in people's hands - that does not, however, make it a better user experience.
Until the user experience has parity with native apps, I don't see it filling anything other than the niche that the Xamarin/Cordava's of the world already fulfill.