It would be interesting if there was an option between public and non-public.
I like the idea of having a private database for my coins. I don't mind displaying them, and even think it will be useful for people to find my coins in searches.
I am not sure I like the idea of people being able to 'google' my user id, and suddenly my coins start popping up. A semi-private choice seems useful, although probably different people have different ideas what fields should be private, so perhaps it's more complicated.