It's like an email address. I've used pidgin, trillion, meebo. I had to know what service a friend was on, generally they'd ask if I had whatever client they originally used to talk to people online with, and went from there.
I may have misread your intent, but honestly I don't see how "user directory" and "privacy" interoperate. What matrix does is maybe prove that you're talking to someone who has access to the same hardware, if not the same person, when you message the same user.
I don't shill for matrix, but I also try to use mastodon to have regular human conversations and I couldn't tell you what service everyone is on...
imagine if we were discussing email today. "how can you know beforehand the email id exists and is owned by the intended person" ? then we would be forced to set up a "to contact with this person, click this link to confirm the secure channel" and other shenanigans
I may have misread your intent, but honestly I don't see how "user directory" and "privacy" interoperate. What matrix does is maybe prove that you're talking to someone who has access to the same hardware, if not the same person, when you message the same user.
I don't shill for matrix, but I also try to use mastodon to have regular human conversations and I couldn't tell you what service everyone is on...