#Amethyst has DMs and public messages. So, it works well as a native chat app. Those are two kinds where outboxes really shine.
I think the outbox model is a bit much for kind 1, if you already have good proxy relays.
I also think that relays getting smarter has greatly reduced the need to broadcast all over the place, as lots of relays stream in and out from other relays.
If you write a public message or an article to TheForest 🌲, for example, it ends up on TheCitadel 🛡️.
And on damus, primal, lol, freelay, band, lumina, wheat, aggr.nostr.land and mom. And lots of other relays stream in from those relays... It's like a mesh.