System Administrators and Administrators with Client Defined Roles allowing them access to edit user accounts can change the primary email of any user that does not have an import record associated with their account. But they don't have the option of changing the primary email if there is an import record on the account (even if imports are inactive, it's just checking the record).

System Administrators are able to set an email alias regardless of the import file, but other administrators are not able to complete this task.

Primary Email field on user account