Creating two-step authentication for yourself, but allowing attackers to have one-step authentication... interesting concept.
This is not a great idea if you have a public profile connecting your username to your email because someone can hack your email.
But you not knowing your password doesn’t hurt your security as far as I can tell.
Your login information can be gained via keyloggers, network sniffing, phishing scams, malware, malicious employees, and all sorts of other methods..
This is why two-factor authentication is so important, to help prevent your account from being compromised in the event that your username and password is.
The way I see it, not knowing your password removes some potential threats around managing that password incorrectly, at the cost of increasing the risk of losing access to your account if the recovery mechanism doesn’t work.
It offers some extra security, but very little. It's the digital equivalent of locking your back door but not bothering with the front door.
The comment I originally responded to seemed to think so.
The username isn't supposed to be a secret, social engineering will most likely be very easy.
A sufficiently large random unknown password is actually significantly less likely to be brute forced than the service itself is to be exploited.