You're seriously proposing that organizations along the same general lines as the EFF or ACLU would be okay with being the implementing partner of a "papers, please" identify verification regime? I highly doubt their leadership would entertain the idea for even the briefest moment.
It can be done with either 0 or 1 "papers, please" events per device rather than 1 per website or worse 1 per website visit, and without preventing anonymous access, but most of the laws do not require that it be done that. Most age verification services will do the minimum required, which usually will mean they are more intrusive and more leaky.
The best way they could ensure that, if they can't convince governments to write the age verification laws to require it, would be to operate such a service themselves.
Even if the tide turns it is going to be pretty widespread before it ebbs. Why not work to make sure before that happens it is done in a way that protects privacy?
[1] https://en.wikipedia.org/wiki/Online_age_verification_laws_b...
Also ICANN should have gotten the corporate death penalty when it announced gTLDs.