For most purposes, you could probably have the phone have a TLS cert for an identity, have the identity provider sign that cert, then use mTLS. No phishing possible because you're not giving access to anything; just proving your identity to whichever server you talk to (and they can't forward that proof).

Honestly I'm not sure why oauth became such a thing and mutual SSL did not. Most "social login" use cases don't need a token that grants any access to anything from the idp. Just proof of id, which could be done in the background by your browser/OS service though some standardized cert renewal process.