8 – Hide the password field during user registration?

I did not enable this option:

[ ]    Email confirmation required when a visitor creates an account

If I remove the check mark, the user must enter a password when registering. The problem is, I want the user to be able to register without a password and also not receive a new login email. This is because a user who logs on to the site can log in immediately. I can not use the blocked state for the user. I need the user to avoid being blocked. And then I added a new "real confirmation" box after clicking on the link in my own custom email.

An even better solution would be if I could use Drupal's login method, but the user can log in even if it's not verified. Maybe there is something that already does this?