I don't think I've ever used a website that's able to run offline before aside from Google Docs (and that requires a browser extension). When the Internet goes offline I close the browser and use regular software where my mind can context switch to offline mode to minimize any risk of being further distracted by an outage that's not within my power to address.

The way I see it, these PWA client-side caching technologies are mostly used by news websites to install permanent service workers on my PC that run in the background after the tab is closed to mitm http requests, phone home every day, and have a kill switch over my data associated with their origin. What's my data? I don't even know. For example, I noticed the Western Digital Forum (I don't even remember visiting it) had a service worker that managed to store 1gb of content to my hard disk. What's in it? I don't know. Chrome doesn't let me see it. Maybe it made the whole forum available offline for me to enjoy. Or maybe I'm an unknowing member of their new cloud storage service. Can't tell. The lack of visibility, lack of consent, and lack of options to disable these emerging standards are in themselves an issue. We should be focusing on making local apps better, rather than having browsers foray into territories that are not in sync at all with expectations.