Many users aren't aware that the email field isn't public because it is visible when they view their own profile page while logged in. While your suggested solution is better, it might be an easier and quicker fix to simply add a note next to the email field indicating that the email address is only visible to the administrators. Then, if a user wanted to make his email address available to readers, he would think to pop it into the "about" field (perhaps with some obfuscation).
If the user enables this option, their email address is shown as an image (or otherwise spam proofed) in their profile to other logged in users.