I think the registration pattern should be - user enters email to register. email is sent to that email with a link to verify. user clicks link. user gets email with username and password to login in to the profile created for them.
same thing in blue which additionally opens the door for someone else to change their password and lock them out, never mind the quality of passwords users set initially etc. Looking at you, mum, registering a new account everytime you forget the last password.