[ghusto]

2FA protects two different attacks: 1) Hacker obtaining your password (through phishing, compromise of third party, etc.) 2) _You_ actually being compromised yourself somehow.

It is still effective for the first protection if you store your codes in your password manager, but less for the second. I say less, and not completely, because if your machine is compromised, gaining access to your phone too is only a matter of time. Of course this can be mitigated why proper hardware tokens, but most people aren't using those.