Just say the quiet part out loud: this is absolutely going to happen, and this is why we need to fight our hardest to stop it.
Stop being distracted by and thinking about the technical points when the whole idea itself is bad, just like WEI and the other authoritarian ideas that originated with "trusted computing".
Seems like a great thing then. People get annoyed, businesses that comply lose customers and money etc.
All that friction means these policies become inherently less popular regardless of anything else. While this crap work effortlessly out of the box is just outright dystopian
The problem with that is that the government obtained logs from the 3rd parties they might be able to compare timestamps with the timestamps of the anonymous age queries and figure out what sites some people were logging into.
The real challenge will be ensuring this doesn't inadvertently entrench the gatekeeping power of major OS vendors or create a single point of failure for identity tracking. However, from a data-minimization standpoint, it feels like a more robust approach than the current fragmented landscape of requiring users to upload sensitive IDs to dozens of different websites.