I'd argue that this is negligible for data collectors and governments. Governments already know who you are and what sites you vist for 99.99% of the population. Data collectors already know who you are and have a pretty good idea of the sites you vist.
What unique information is this going to give the government and data collectors to abuse? Lets establish one case that both affects average people and is "bad" and not waste time discussing things that only affect a tiny minority of privacy minded people.
Keep in mind the law states a platform must provide multiple ways to reasonably verify a user is older than 16. No mention of giving the specific user age or requiring govt id