I was having an argument over 1password's 2fa support not being a second factor. (I don't think it is.) However, it is so much safer than not using 2fa. In similar terms U2F is amazing and keeps you from being phished and has a great challenge/response protocol, if that was implemented in 1password (or browsers themselves thank you!) we'd all be a lot safer than not using it at all. In 2018 I'm using an app to take s…
Afaiu 2fa primarily protects from password leaks on the part of the service and coincidentally some other kinds of leaks such as keylogging. Not so much from data theft on the user's side. A different question, though, is whether a password keeper web service could leak passwords like any other service.
2FA is meant to protect primarily against phishing. It happens to protect against some other attacks as well, but phishing is the primary motivation.
That's why physical U2F devices are considered the gold standard of authentication today - it's possible to phish a TOTP code, but it's very difficult to phish a U2F signature, and impossible to do so through a scalable, automated attack.