Nobody is “cut”, they decide on their own not to pursue it anymore (probably recognizing it would be futile, or because they’ve lost/changed interest). I would tend to agree that attending a very competitive school full of really bright kids can make success harder. Malcolm Gladwell gives an example along those lines in his book “David and Goliath”. There is a brief summary at http://www.businessinsider.com/malcolm-gladwells-david-and-goliath-2013-10 As for cutthroat, sure, try and avoid that, although you’d not want to trust just one or two kids opinion about this.
Hats off to Hamilton for writing letters for all kids who want one. Some schools do this, they should be honored and those that protect their yield excorciated. That said, though, I think this is an example of starting with great kids as I mentioned previously. The Hamilton average SAT score was 2070, or 96th percentile. These are pretty smart kids.