BuddyPress.org

The plugin works with or without any other trickery; it uses the email in the database for authentication and ignores the username. Try it on an unmodified installation. Works fine.

The username is unnecessary. That’s why many modern sites don’t use them anymore. In WP/BP you still need something in the username database field because all kinds of functions rely on it, like the profile URL in BP or the ‘forgot password’ process. So you can’t just remove it entirely.

My solution is to generate a username onkeyup from the fullname via Javascript on the registration form, hidden from view. In an earlier attempt I used a script that just autogenerated a gibberish username.