Yeah, that is one of the reasons for PWA, & it also offers proper cache features for a better app-like experience.
Regarding Nostr, nostr protocol is indeed a flagship idea like Bitcoin blockchain, but the clients are more like Bitcoin wallets. Imagine having just one wallet that everyone uses, and it being custodial.
I mean, clients can essentially do anything, barring banning any piece of content, regardless of how many relays you are connected to. That's why people are very careful.