I mean tbf, I think if your kid is smart enough to work out they need to log into the router to change the DNS settings then they can probably figure out how to set it on their end device too. Unless you’re also blocking VPNs and non-dhcp directed DNS requests too.
I think the obvious solution is to force router makers to have a more user-friendly way to enable child-friendly features (we did that with TVs, why not the internet?) rather than forcing websites to either shutdown or do sketchy shit like take IDs. I work as a tech for an ISP, I assure you most people can’t figure out (or are barely able to even with instructions) how to change the default wifi, there’s no chance in hell you’re gonna explain to them how to point traffic to a custom dns.
Personally, I remember chrome always flash banging me when on a website with a dark background and I clicked to the next page because apparently clearing the page to the same RGB value as what is set as the HTML background is too hard so they just always clear with pure white. But they did have a faster JS engine. Not sure anymore, haven’t given enough of a shit to try anything but firefox in years now.