It’s mostly just that I don’t want the government to know precisely which websites I visit. Nor do I want the the porn sites to know exactly who I am.

I understand, I want that too. It’s easily possible though (just one example for a scheme):

• you visit porn site
• porn site sends your browser a random nonce
• you/browser tell government service: sign this if I’m >18
• government signs the nonce + a timstamp to prove freshness
• your browser forwards the result to the porn site
• porn site can verify signature per standard public certificate chains
• now porn site has proof that you are >18, but knows nothing else about you; and government only knows that you wanted proof that you are an adult, but not for what site or purpose you wanted to prove that

Alternatively, if we go the “device has an age bracket field browsers access” route, it’s even simpler, and just as if not more privacy preserving.