Honestly, I'm all in for PWAs in favour of Chrome Apps. To the final user, a PWA will work the same: an icon and a chrome-less window. However, they are built on top of open standards, so any browser can support PWAs and provide the same experience to their users, unlike Chrome apps, which only were supposed to work in Chrome. I hope that in the transition, we see more and more progressive web applications.
PWAs have replaced a few native apps on my phone and I couldn't be happier about it. I can use Twitter, Telegram, YouTube and even read HN (via the Premii webapp ) through a fullscreen interface that behaves like a native application (no address bar, tinted notifications bar, push notifications for Twitter and Telegram), but that nonetheless is still a browser.
Support for PWAs on Firefox for Android is around the corner. I'm a Firefox Nightly user and the support is there: websites that have a webapp manifest display an icon on the address bar to let you quickly "install" the application as an icon to the homescreen. It is supposed to reach stable channel on Firefox 58 .