Don't underestimate the grassroots popularity of these measures. Look at any Hacker News thread regarding age verification and you will find a lot of comments coming out in support of age verification. Most of them are assuming that age verification is something that will only apply to sites they don't use like Facebook.

There are a couple parallel moral panics intersecting on this topic. Again even on HN you'll find people parroting dodgy statistics about child trafficking on social media, proclaiming that short form video is equivalent to highly addictive drugs, or making sweeping claims that under-18s should be banned from having smart phones. It's apparent none of them ever considered that the age restrictions they've been inviting might apply to something they use. It's always assumed to apply only to the kids on the TikTok or something.