Email Address as Username: Changing an Email Address

I've looked into some plugins that will allow me to force users to use their email addresses as usernames and I've been happy with the integration so far. But, I've run into an issue that I can't quite figure out and that I want to figure out before our new site goes live.

As far as I understand it, WP usernames, once they're set, cannot be changed easily. So, what happens to a user whose email address changes? If their username is set as their email address this poses a problem.

Are there other ways around this? I could change someone's user name through PHPMyAdmin without causing too much harm but I don't, of course, want to do that every time someone changes an email address. There's also the "Username Changer" plugin but that again seems to be controlled by me. I want it to happen automatically whenever someone wants to change their email address.