No, it's not the same. There are anonymous solutions that solve this problem that are perfectly acceptable. Not perfect for prevention, but a good compromise nonetheless. Like cig/alcohol underage consumption prevention.
I think we totally disagree on the degree of how much this is actually a problem compared to how much we're willing to invest in it. Those anonymous solutions are fairly idealistic and Nirvana-esque themselves, I don't think they'd see wide adoption. Beyond that I'm firmly in the camp that age verification for the kids is a complete smokescreen for the actual intent of these efforts, which is more surveillance, so on principal I'm opposed to any movement in this direction and doubt we'll find common ground.
There is no such thing as anonymous age verification in practice.