Don't get me wrong, I'm all for privacy. But between setting up the birthdate when creating my children's local account on their computers, and having to send a copy of their ID to every platform under the sun, I'd easily chose the former.
I'd even agree to a simple protocol (HTTP X-Over-18 / X-Over-21 headers?) to that.
The Califirnia law, at least, states the age flag should be set when the account is created, presumably by the controller of the computer, and holds that controller responsible for setting it correctly, and the developer responsible for ensuring it's set and works correctly, at least, that's my reading of it. If it's your computer, that makes you resoonsible for setting your age and that of accounts you create for your children.