Oh they actually do. The thing is that people already have all the apps what they need, so there is no regular need to download other apps. But when such need arrives though, they head to the appstore.

The reality in developing countries is actually completely opposite. People in those countries love apps and use WiFi etc. to downlod them in coffee shops/schools/offices... so they can keep using the service only by downloading the minimalistic json instead of downloading whole service with UI/GFX etc. each time they need it.

I tried using some of those PWA now online and they do work better than traditional webapps, however they are still slightly laggish and have unfinished feeling when compared to native apps.

PWA is going to be almost certain flop. It's trying to do almost same what React Native has already done but with PWA you have to convince the users to switch from the secure, trusted, well working apps to "inferior and unsure webapps" and from just pressing the app icon back to the old school "open browser, select address bar, enter address, press enter"-hassle. Changing this mentality that people have build for almost 10 years now is probably going to be as easy as to make Trump change his opinion about the wall.