I fully appreciate that you care more about anonymity on principle, but it seems very naive to assume that principles are necessarily going to win out over the demands of aggrieved reactionary parents. Cranky parents are very consistent voters and providers of tax revenue in most polities and politicians want them to be reasonably happy and quiescent for the sake of stability. It seems to me you are wildly underestimating the size of your potential opposition.
Are aggrieved reactionary parents demanding that they should have to scan their face to look at websites? It seems to me like they just want social media companies to be forced to change their harmful and predatory practices and that instead of properly regulating the bad behavior of social media companies the government has decided to use this issue as a means to give themselves more surveillance and control.
We don't need to make parents the enemy of our online privacy. We just need parents to reject the idea that they have to give up their identity and the identity of their children to every shitty social media company and shady website on the internet to "protect" them.