That prevents the site from knowing your identity, but I'm not convinced it prevents the government from knowing you visit the site. The government could keep track of which document corresponds to which individual whenever they issue / sign it.
So if the government mandated that each signed proof of "age>18" was stored by the service and mapped to each account (to validate their proof), then the government could request the service to provide them copy of the proof and then cross-check from their end which particular individual is linked to it.