There's already authorities that know your age, so verifying age with them to get the credential isn't the part that needs to be anonymous. The issue is them knowing what you do with your credential, which anonymous credentials solves by making it impossible to track tokens back to the credential holder. As far as sharing, there are some possible mitigations.

Right. And the possible sharing mitigations generally amount to tracking.

This isn’t even getting to the issue that mandating government-issued credentials is the “foot in the door”. If you mandate the use of government creds for accessing websites, it’s an obvious step to turn around and demand that sites report credential use to “fight credential fraud”.