The government still knows your identity in this scenario, so it's a pretty limited form of anonymity (i.e. only suitable for activities the government isn't hostile to)
The only thing saving you from a hostile government is a well educated populace that really wants democracy and is willing to fight for it (through constant activism, peaceful & other types of protests). This is where many democracies are failing now. No amount of technology or rules can replace large amounts of constantly vigilant eyes that understand how democracy is subverted.
I would rather optimize for not giving companies too much power and end up with a Kafkaesque patchwork of corporate abuses and regulatory captures.
The organisation asks the govt, and gives back a signed token.
The the only thing the government knows is that an age verification was requested. Once verification has been done once for one site, it can be used for future verifications.