I have been doing this on our site by banning people who want to have their profiles hidden. It's a terribly inelegant solution as 1) it sends the message that they aren't welcome, 2) they need to send an unban request to chang this "setting" which many won't know to do, and 3) I don't know if there are more who prefer their privacy that aren't speaking up.
To extend it further, other fields could be displayed selectively on profiles. For example, I have email not displayed by default, but some would prefer it made available. Likewise with addresses, phone numbers, etc.
I'm trying to use CB as a membership manager, and these features would go a long way toward that end. it would be great for my needs.