The problem is that it is much easier to implement such a check in a way which lets the verification service link the site to the user, with no discernable difference to the end user

e: I get the same feeling as I do reading about key escrow schemes in the Clipper chip vein, where nobody claimed it was theoretically impossible to have a "spare key" only accessible by warrant, but the resulting complexity and new threat classes [1] just was not worth it

[1] https://academiccommons.columbia.edu/doi/10.7916/D8GM8F2W