I am sarcastic because this discussion is about a different attack. Not about fishing.
(The OP says one time codes are worse than passwords. In case of fishing passwords fail the same way as one time codes.)
I was also sarcastic/provocative even in the prev comment, saying the GOOD site always includes a warning with the code making the attack impossible. A variation of the attack is very widely used by phone scammers: "Hello, we are updating intercomm on your appartment block. Please tell us your name and phone number. Ok, you will receive a code now, tell it to us". Yet many online services and banks still send one time codes without a warning to never share it!
The fishing point may also be used in defence of one time codes: if the GOOD service was using passwords instead of one time codes, the BAD could just initiated fishing attack, redirecting the user to a fake login page - people today are used to "Login with" flow.