Clients should nudge users towards using such relays for DMs, and that is happening right now in every client.

Relays were never meant to be dumb in the sense that they wouldn't have any internal logic, that was an unfortunate choice of words and a huge misunderstanding that damaged Nostr a lot, it's a surprise to me that people could have thought a relay would be really that dumb, do no filtering, no access control etc and Nostr would still work? Nostr would never work if it was like that.