The same applies to effectively all possible solutions for age verification, no?

Even if you have a perfect mechanism, 17 years old can create real age-verified accounts and then sell the username and password afterwards. Selling age-verification tokens directly would likely be harder than just swapping those login details, since it's very easy to make the tokens time-limited (in practice normal use would probably be some kind of oauth-style redirect flow, so they'd really only have to be valid for a few seconds).

This same argument applies to adults buying alcohol for teenagers too. The determined teenager with money can definitely find a way to get alcohol, but it doesn't mean the age restrictions on purchases are pointless.

Imo it's a bit pointless to worry about high-speed black markets trading in signed tokens when the current most common alternative is a popup with an "I promise I am over 18" button. If society agrees some things should be difficult to access if you're underage, then we can definitely do better than that as a solution.

Germany has a system in their ID cards that allows anonymous age verification. No one uses it but it’s a technical marvel in my opinion.

The site asks for specific read permissions and the user can decide if he wants to grant them.

One of these permissions is age verification.

You put the phone on the ID card and there is a cryptographic proof that the user connecting to the site is in possession of an ID of a person above 16 (which he of course could have stolen).

So it is technically totally feasible to have good data privacy AND age verification.

this is the same argument as "why have government id cards, someone could just use a fake beard and use their older classmates id". Any system allows for some gaps, similar to how creditcard transactions make transactions safer but on either side of that transaction there some "insurance" and some leeway if someone really wanted to.