I don't understand why an installed PWA should not be able to keep their storage just as a "normal" app can. It would clearly be better for both developers and users. There are so many apps & websites that could be more privacy friendly if they could just trust localstorage to actually be "storage".
Most users are asked to install multiple apps for the normal sites they visit (like news sites, social media, imagehosting and more). They usually don't, and that's good. Those apps should not be apps, they should be websites. Most of those apps can be a simple website. If the users want/need more functionality that can be within a installed PWA.
I think this is more people and developers fetishizing what it means to be in the app store or to be "native". If we can run it all in probably the best sandbox we have available without having vendor specific builds or vendor specific prompts why would we as users or developers want anything else?
Some apps should be native. But the majority of them would be better as webapps rather than android/iOS apps.
EDIT: Also I'd argue a lot of those problems are artificially created by the platforms, not the developers.