There's no such thing as private or anonymous age verification. It doesn't exist.
The problem with this whole thing is the expectation of privacy online for interactions where their IRL equivalents don't have such an expectation. Even if there was no harm being done to anyone, it isn't a rational argument if you subscribe to the ideal of equal treatment under the law.
Governments are banking on being able to purchase that site visit data anyways, bypassing their own laws that prohibit them to do surveil, we can require them by means of technology to comply with laws and for the last time resolve the "but the children" argument.
This is not in any current (proposed) laws I'm aware of.