If you don't verify identity it's easy to fake.

it doesn't matter!!!

it's a parenting tool, not an online banking system

EDIT: Also the most relevant devices are not laptops, but phones, tablets, gaming consoles. Some of them have such a system already working "good enough" for the use cases of "games"/"game stores" and similar. Yes not browser. But very much extensible to that.

Giving parents control of child mode is much better than the state deciding. If Parents want to fake the ages of their child, that sounds good to me.