A member of my forum recently asked about this, some features that should be working even for private profiles are not displaying on the user card.
They mentioned the topic filter for the user, and sending a direct message. I think the latter should still work with a private profile, except if the user deactive their DMs from everyone?
So I think, UX-wise, those features unrelated to private profile should still be accessible on the user card, unless deactivated for the DMs.
Thanks for everything 