W3C Verifiable Credentials [1] does almost exactly what you suggested and was recently approved as a top-level W3C standard. Adoption has been sluggish outside of digital identity (with Android [2] and the EU digital identity wallet being notable exceptions), but I think it is because the family of standards is relatively new.

[1] https://www.w3.org/TR/vc-overview/

[2] https://developer.android.com/identity/digital-credentials