The privacy issue has two facets, when I show ID to get in to a club or buy alcohol, the entire interaction is transient, the merchant isn't keeping that information and the issuer of the credential doesn't know that happened (i.e. the government).

Just allowing a service provider to receive a third party attestation that you "allowed" still allows the third party to track what you are doing even if the provider can't. That's still unacceptable from a privacy standpoint, I don't want the government, or agents thereof, knowing all the places I've had to show ID.