The students gaining admissions to top unis are largely self-motivated, extremely smart, and would have chosen high-quality activities on their own.
Looking back at my own childhood, I chose my sports, music, and other activities. My parents enabled them, but never forced me into them. Would forcing me to play an additional sport, or forcing me to attend after-school tutoring made the difference between UVA and Harvard? I doubt it. And what did attending UVA instead of Harvard cost me? Hard to say for sure, but I'm inclined to say "not much" as I'm happily upper-middle-class as it is.
And considering my high school peers who did attend Ivies and similar, most of them either smarter or harder working than me.
I remember reading a study about this exact topic and it turns out name brand has little to do with career success in meritocratic career paths - i.e., upper-middle white collar professionals such as engineers, doctors, lawyers, etc.
I guess my conclusion is to be aware of your child's personality. If they aspire to be an engineer, they could probably go anywhere, even gasp Virginia Tech and do fine. However if they aspire to be a politician, then they'd probably be best served to attend the highest grade institution they can so they can be socialized into that in-group.
Flashes back to massive football losses... "It's alright, it's ok, we're gonna be your boss someday!" College students can be such insecure jerks.
(but, yeah, totally agree - the vast majority of students will do just fine with a degree from Big State U)
Also, I do find it bad when parents push their child from an overly young age into some specific thing, but at the same time the reality is, that both physical and mental development improvements in such a young age have a really profound effect. So looking at a 5 years old play the violin is sad in one way, but at the same time at his/her teenage years he/she can choose (at least hopefully) to continue the efforts and with an inner motivation he/she can have a bright future, much more than only starting it at 10+ years old.
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.
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.