I think your guess would be wrong, but I also don't think overbooking is a problem.
As a child who had lots of free time due to living in a place with a lack of structured activities for kids, I really envy kids who can take advantage of such resources enough to have a packed daily schedule.
It's not so much that kids shouldn't have structured activities; it's that these activities shouldn't be thrust upon them by parents.
Yeah, the smaller the kid, the more direction they're going to need. But a 5th grader should be able to pick their activities within reason.
I mentioned it in another thread, but when I was coaching youth sports, I saw two huge (IMO) problems... first, kids specializing at a young age - 5th and 6th graders playing a single sport 9+ months of the year (vs mixing it up). Related to that was a disturbing frequency of overuse injuries in younger athletes. Baseball players coming back from summer with stress fractures in their spines from too much pitching practice and things like that.
And also a whole lot of straight-A students being forced to attend extra-curricular tutoring. I'm sure in some regions, it might be necessary to learn advanced subjects, but Fairfax County schools have robust GT/AP/honors programs and allow dual enrollment at the local community college - very few kids are running out of available maths classes, etc.
And with a robust state college system (UVA, W&M, VT, GMU, JMU, and on and on), the "penalty" for not getting into Stanford isn't much (for the majority of subjects).
Anyways, all anecdotal, but of my son's peers, the kids with the overbooked schedules didn't really go to colleges any more prestigious than anybody else. Most just ended up at one of the several excellent state colleges.
As a child who had lots of free time due to living in a place with a lack of structured activities for kids, I really envy kids who can take advantage of such resources enough to have a packed daily schedule.