I know this is old, but there’s now a “Change the email for another user” action located at:
Workflow -> Click here to add an action… -> Account -> Change the email for another user
Yes, this is cool but sensitive functionality. It requires the user to enter the original password. To make it tighter you could create your own form of security questions. If you do, you would have to perform this gatekeeping before you call the Change Email workflow… of course.
Sometimes users create accounts with incorrect emails and are stuck. You would have to judge if you want to allow this functionality before they are able to email-confirm. As they won’t be able to perform the email confirmation on the wrong email.
This is old, but now Bubble has the option of changing email in several ways. In Workflows, Update User Credentials, under the Account tab, allows one to update both password and email.