The beauty of a protocol like nostr is all kind of apps can browse the "nostrnet". A big heavy do-it-all apps and also lighweight low bandwith optimized ones. At this point the most attention is given to the former (as far as I can tell) because it is all new and people want to try stuff.
That said I think that a ligh nostr browser is very important.
With bad internet, Damus (for example) is a terrible experience. You have no idea if anything is loading while staring on blank screen or missing replies. So it is hard to know if you're just waiting for notes to load or there is nothing to load.
Would a manual pull - push work in extreme cases? Sort of like a offline mode, where you download a specific note structure, reply to everything offline and then push (broadcast) it once you are online? Dunno.