Register email as username

Emails can not be used as user names as wordpress uses user names by default as part of urls (for example the author page). Therefor it is not enough to let users register with email addresses, you also need to have some code to handler the URL related issues.

Anyway this sounds like an XY problem. Since users can login with their email address why would any one actually care what is their login handle created at registration time? The most simple thing to do is to create a registration form in which you create a “sanitized” user name for the user based on his email if you do not want him to think of one.