Yeah, it's just a CYA thing more than a deterrent. Helps keep the site owners from getting sued by parents who weren't supervising their kids.
And yeah...we've probably all done it. I used to pick some random date from the 1950s.
Also this. I was kind of proud at first when I was old enough to honestly tell those things my birthdate, but it's at the point now where they just make me feel old.