What are private client-side PWAs anyway? Good question. The definition of a "progressive web app" is vague. What they seem to mean is a web page which, once you visit it, is cached locally, and thereafter runs locally. The web page accesses various servers, not necessarily ones from the same domain as the web page. Persistent state, if any, is stored locally. The page gets its own icon on the home screen somehow, so…
This is part of the motivation. The other is advertisers using persistent local storage to track users [1].
[1] https://clearcode.cc/blog/alternatives-to-cookie-tracking/