These kids likely will go to elite graduate schools anyways.
A Duke scholar could have better chance to attend Stanford GSB or Medical School (or for that matter HBS or HMS) than an average Stanford undergraduate. That will almost be a sure bet.
In the traditional career paths, S & D are quite equivalent.
S does have a noticeable advantage in engineering/CS/startup. But a kid may very well follow the startup path after graduate school (say MBA). So really the downside is not that much.
Especially for the medicine route. It's better saving the money for medical school.
