People on the other end will only see your message if they are using a client that supports nip-11 DMs and have set up inbox relays. This problem is solved by getting everyone to start using @0xchat.
By continuing to use nip-04 DMs, everyone will keep leaking metadata and some people might not even know it. This can be really bad for some people.
I’ve seen someone zap an anonymous DM which is pointless. Anyone can figure out who sent the zap cause you can clearly see who’s talking to each other in the DM. Anon zapping a public note is more private than sending an anon zap on a nip-04 DM.