i.e. you have to check imperial.ac.uk/.well-known/auth0-vc.pub or whatever, and if that matches, still all you know is that I have the key (or device, whatever), not necessarily that it was truly me. And if you don't check the issuer (or don't trust it's claim - impeerial.ac.uk says that the bearer has a degree from imperial.ac.uk for example) then it doesn't tell you anything.
Of course that's not really avoidable... but I can't think of a use case for this that doesn't just reduce to 'the issuer may as well just publish the contents' - it's useful when you want to only selectively share a credential from party A with party B, and it's something that B has reason to doubt/verify... but I can't think of an example?