We have the technology to do age verification without revealing any more information to the site and without the verification authority finding out what sites we are browsing. However, most people are ignorant of it.
If we don't push for the use of privacy preserving technology we wont get it and we will get more tracking. You cannot defeat age verification on the internet, age verification is already a feature of our culture. The only way out is to ensure that privacy preserving technologies are mandated.