I really like the idea of PWAs, but I've tried a few of them and I always come away being annoyed at the app launch latency. They still feel like they're hitting a remote server when starting up for.... something? My uneducated hunch is that they're over-zealously checking their server for updates.
The other issue I have with their implementation is the opaqueness of how offline caching works. How much space do apps get? When does the offline cache get invalidated? I care about that because of that terrible launch latency.
I think these issues can be attributed to PWAs being second-class citizens in Android and iOS.