Not necessarily. A festival is a good example: the venue operates a relay & only accepts notes posted by people who have write access via invite code on their ticket or something. People are posting & sharing what's going on at the venue with eachother & only viewing eachother's notes, but they can still switch to their home feed to see if the babysitter is actually playing on their phone instead of cooking dinner.
Meanwhile, anyone following the attendees is also seeing what is being posted... cuz outbox. They think it looks fun, want to attend the next festival, whatever... they can reply & stuff... cuz outbox.
The venue doesn't have to worry about partnering with a client or having their own app and all that. They can wipe it & reset for the next night. Attendees don't have to worry about installing another app. They can just sign in & use whatever relay feed supporting app they use & go.
Any place or thing could have its own live social media feed instead of or in cunjunction with a typical website. It's kind of curated but not really. Things just aren't that far along yet. Curation, algos, and interesting ways of interacting are a good start. Sorting & discovering needs work but there needs to be enough relay diversity to do it.