The feature to follow on email verification is here: Account recovery with password reset.
Features
Account recovery
The login screen now has a blue link below the password:
Problems logging in?
Clicking this link will open up the Recover account dialog, where you have two options to identify yourself; By Account name or by Character name:
Once you’ve entered one of them and clicked Recover account, a mail will be sent to your verified email address registered to the account. If the account has no verified email address, no mail is actually sent even if it says so.
If you’ve selected to recovery by Character name, the mail will also contain the account name:
Clicking the Reset password button will take you to a Reset password page where you can reset your password:
The entire flow should allow for safe resetting of passwords.