I strongly believe that most would actually. All parents I've talked to have had issues with parenting their children's online activity. They know there are harmful things they want to prevent them from accessing but it is simply to hard to configure and set up existing tools for it. (Besides every single friend they have don't have any restrictions so it all seem pointless.)

I can also see also large support for uploading ID to various services when talking about kids, but when you re-frame the question to adults, most seems to really dislike the idea immensely.

Sure there will be children with access to unrestricted devices, just like we had kids with porn mags hidden in a forest somewhere back in the day, or how that one sketchy guy was buying alcohol, etc. But I think this is an acceptable level of risk for whatever harm people want to prevent.