I'd like to have a TON of other profile fields, but then allow the user to select which fields they'd like to be visible via a checkbox next to the field. This way, the site users can obtain/require more information about their users, without others seeing info that the visitor doesn't want seen?

Anyone have any thoughts on this?

I've done stuff like that before.
Basically you need a field for the info and another field to indicate if it's on or off (displayed or not).

When the profile is shown to a non admin, you use an if statement to check the "displayed or not field" to determine if you're showing it or not showing it.