Giving fake info adds noise to the mechanism

Yes, but in this case which we're discussing:

It may often times be trickier than that - content often mixed of course. My 10 y/o hit me with a request yesterday to play Among Us where the age verification system wanted my full name, address, email, AND the last 4 digits of my SSN. I refused.

The bad actor still gets ROI, eg 'paid', for another bit of user data.

Making the overall system less useful is good. However, not allowing a company to profit, and giving fake info still allows for that, is paramount. EG, even with fake info, many metrics on a phone are still gamed and profitable.

That's why they're collected, after all. For profit.