Isn't 'always connected' and 5G going to take care of the 24/7 accessibility issue eventually? Also, I thought I read somewhere that notifications via Edge/Cortana where on the to-do list for MS:>)
Well notifications via edge in itself may or may not do it, depending on whether they write the service worker. That could be good news, but the PWA gets wrapped as a UWP, and I think it runs independently from edge. Or that's what I heard.
5G really doesn't help offline or low network access at all. The current tech depends on multiple carriers on multiple frequencies - Ie it will only be available in dense population areas.
That said, offline access really isn't a big deal for PWAs. Basically anything you'd use them for (like the current examples of twitter and uber), you want to do online anyway. For stuff you'd actually want to do offline, like a game, or a map, there are full UWPs.
Notifications are the only big deal. Personally to be, there's very few apps I really want notifications from. Twitter isn't really one of them - for me. Uber would be nice to get notifications from, but if your calling an uber, you can just leave the app open.
So it's not a killer, but it would be nice. I kind of like to think, that if MSFT doesn't make a service for notifications, that some enterprising win mobile enthusiast could. When blackberry stopped supporting blackberry, a coder fan made an app suite that helped users install android apps better.
I think PWA serves the same purpose for win10m - it will keep the ecosystem going long after msft has stopped supporting it themselves. And much better than the android installs did for blackberry for that matter (because for them, the android engine version has really dated, whereas for us, PWA is just getting started and is backed by everyone)