If you needed a serialized representation of structured data, I think it made engineering sense to use XML even if it was more featureful than you needed. The alternatives were ASN.1 or rolling your own format from scratch. It's not at all obvious that those are better.
(You could argue in favor of rolling your own format on the grounds that it wouldn't be vulnerable to XML-specific security problems, but I don't think those problems were fully appreciated at the time. If they had been, probably people would have come up with some kind of quasi-standardizable secure XML variant that just disables the specific features that cause those problems.)
I agree that XML (even without the security-relevant misfeatures) is worse than JSON or other non-markup-language serialization formats for the majority of use cases that don't need a markup language, but this is not a big problem, it's basically just syntax.
Smaller tech companies don't want federated login to happen. They are, as a rule, far to happy to rely on the SSO tax to up-sell enterprise customers. The major authentication companies don't want federated login to happy because it invites more competitors and threatens their absurd margins.
Until someone manages to solve the business side, no amount of improved technology will change a thing. I'm pretty sure the few small interoperability gaps OpenID Connect has could be corrected in a matter of months if the stakeholders actually cared.
From vague memory, the other stuff in OpenID Connect was layered over the original OpenID identity verification part.
IndieAuth exists, it's just not widely supported.
It’s like “using JSON” but actually encoding objects indirectly through your own made up object notation… that is structured.
"Host your own identity"