I feel you are talking about a different thing now. My point was surrounding what you initially said:
The only right way to do this, is if governments provide their citizens with an eID that any site can ask “is this person 18+?” and get an accurate answer without any other identifiable info. And if you don’t want the government to know what sites you visit, have sites route the request through a proxy.
An eID is a digital document. You yourself are proposing that sites should request people to provide a document, one that's issued by the government to you, personally. Then later you said that using a proxy prevents the government to know what you visit.
My answer was that if you are providing a government-issued document/file to the service then the government (the issuer) can know if you visit the site just by keeping track of who did they issue each document for and requesting the sites for copies of the documents. Even if the document itself does not say your name. And that's regardless of how many proxy layers you use, since there's traceability in the document. This makes you fundamentally less anonymous to the government than before (when you could have indeed used a proxy to prevent this), this makes proxies no longer a good defense.
The service does not know you, but that's not the point, what you said is that the government can't know if you visit the site, which is the one thing I disagreed with.