I personally use 1password for authenticator codes - highly recommend if you haven't seen it: https://support.1password.com/one-time-passwords/

Edit: Didn't answer the actual question - it's something we can look into. My instinct is that offering this wouldn't drastically change the security model, as long as we can be confident your password actually came from a secure password manager. Since some password managers (like 1password) are very strongly tied to devices, I think your ability to retrieve a password from it is a reasonable proxy for a possession factor.

It's definitely something I'd want to read more literature on before building. That's just my instinct, and I'm half expecting someone on HN to share the attack I'm forgetting :)