Any idea that is based on "If everyone just..." is wishful thinking. Describe the mechanism by which you convince everyone to just do something.
Sure, but the ID solution is an "if everyone just gives up their privacy / anonymity / sensitive data" and the mechanism is by denial of service
In fact its worse. Every site must also implement this security check. Or everyone must agree to just use sites and services that follow this policy. Otherwise anyone can just use another, often 'less safe' website.
Pass a law that requires devices and software to support a per-device or per user account 'child' or 'minor' flag. The flag must be lockable with a password or another account. Pass a law that mandates that websites and content handle the flag appropriately, whether that means denying service or limiting access.
This would protect children while only minimally infringing on privacy.
The mechanism by which we make everyone 'just' is laws. The laws that are being passed are telling of the actual goals.