User name field could be hidden with anonymous checkout as login option and not using user name as e-mail

When using the following settings:

1. Continue without register: YES
2. Use username as order email: NO
3. Use anonymous checkout as option to login form: YES

the user name field is visible at the login form (even shows a required asterisk), but it's value will be ignored when continuing without logging in. I think this field can confuse visitors and thus could be initially hidden, just like the password field is. But when both the user name and password fields are hidden, the field's title "Do you have a password?" could also be changed into something like "Do you have an account?".