Even with ZKP this is still highly problematic, it create difficulty for undocumented people to access the web, create ton of phishing opportunity, reinforce censorship on most site (as they will now all need to be minor compliant or need age verification), reinforce the chilling effect and make the web even less crawlable/archivable (or you need to give a valid citizen ID to your crawler/archiver).

With no proof it will protect anyone from proven harm.

>it create difficulty for undocumented people to access the web

Why is this such a sticking point in US politics? If the "undocumented" people aren't supposed to be in the country in the first place, why should rest of society cater to them? Even if you're against age verification for other reasons, dragging in the immigration angle is just going to alienate the other half of the population who don't share your view on undocumented people, and is a great way to turn a non-partisan issue into a partisan one. It's kind of like campaigning for medicare for all, and then listing "free abortions and gender affirming surgery" as one of the arguments for it.