OpenID Connect Core, section 2: "The ID Token is represented as a JSON Web Token (JWT) [JWT]." (https://openid.net/specs/openid-connect-core-1_0.html#IDToke...)
I've got to say, I've seen providers without proper discovery, I've seen providers with strange hybrid flows and I'm pretty sure most providers don't implement the request/response signing and encryption (after all, if you want insanity, you'll be more than happy with SAML). But I've never seen a provider who doesn't implement an ID token.
I think everybody would agree that OpenID Connect without an ID token is just plain OAuth 2.
I've had providers with the id_token and access_token being the same value. Other where they were different values. One that didn't support refresh_token at all.
Then a variety of screw ups where the required claims in the JWT tokens are missing or incorrect.
It's wild really. It always takes a bit of work to integrate any OpenID Connect provider. Most libraries only care to handle Google or Facebook login.