I believe the goal for Damus is to have a local-first integrated relay.
Android has one you can run on your phone that works with any native client you also run on your phone, thanks to greenart7c3 (npub1w4u…0jr5) . It's called Citrine.
Not sure which approach I think is best. If you only use one client, then building it into the client might be the way to go. If you use multiple clients, then building it into every one of them doesn't make sense. Better to have a separate relay app that all of them can access.
When it comes to having a relay that others can read YOUR notes from, the difficulty is in securely exposing a local service to the broader internet, and the fact that even at their best, phones have limited bandwith, battery life, and intermittent internet connection. It is much better to run an outbox relay on a server than on a phone. Though, technically, you CAN use Citrine as an outbox relay when paired with Orbot, but it would only be accessible by others via Tor, which would be audience limiting.
