On the one hand, you want the ban to be effective. On the other, you don't want to share any kind of ID with social media companies, nor expose one's internet traffic in case a government database is leaked.

It seems to me that ring signatures are the best suited tool here. The steps would be as follows:

1. A user generates a private-public ring signature pair
2. A user shares one's public signature with the government, along with their ID. The signature is stored in a publically accessible database of signatures belonging to adult users
3. When the user wants to access an age-restricted platform, he/she queries the database for a random selection of public keys.
4. The user combines the keys together with his/her private signature, and issues an authorizing request. By the design of ring signatures, so it's impossible to tell which adult user from the random selection hashed it.

The restricted service can be accessed without identifying oneself. Even in the event of a government signature cache leak, users’ online activity would remain untraceable.

What do you think of this idea? Can you think of a better way?