I went hunting in the NIST documentation to see if this is even an approved authentication method and, technically, I can't find anything wrong with it (if we consider it to be a "Look-up Secret Authenticator", see NIST 800-63b section 5.1.2.1). They're technically abusing what is supposed to be a collection of pre-distributed authenticators (think recovery codes), but there's nothing prohibiting these look-up codes from being sent on-demand and there only being a single selection.

As for the method itself.. IMO they're certainly phishable, but I don't think they're any more phishable than a typical username/password prompt.

> An attacker can simply send your email address to a legitimate service, and prompt for a 6-digit code. You can't know for sure if the code is supposed to be entered in the right place.

An attacker can also simply present a login prompt, say a Google-looking one, and a user will just enter their credentials.

This is why phishing-resistant authentication is the one true path forward.