In my experience, the "top tier of kids" is more cultural than school-specific. Even in schools like TJHST there's usually 10–30 students in the school that really care about achieving, while the other 90% don't put in much effort (beyond your typical public schooler). There are a few feeder (public) schools on the coasts, but most of the private schools differentiate by extracurriculars (fencing, rowing, horseback riding) rather than academic excellence.

Accelerated tracks would produce the top tier, which begin in elementary school - so it's a matter of how much your parents invested in your education before school. Any child can technically enter the accelerated track at any grade. The later they join, the more untaught expectations there are. The other students went over these things already in previous accelerated classes. There's no on-ramp.

In the normal track, you don't eventually take calculus in math, learn much about labwork in science, or even learn how to write a research paper until the last year of classes at 18. (Source: class of 2005, USA)