Val, I see your point, but also consider-- kids who are well-rounded and high LOG may well be polymaths who couldn't bear to "give up" even one of their many EC's to "focus" on something that has more bearing on their putative future career path.

I'm loathe to suggest that kind of system, having seen how HAPPY it makes my own little PG polymath to be completely engaged in something that has no outside significance in her life. It's purely for the joy of doing it, if that makes sense. That is, I can't actually see her majoring in anything outside of STEM, but that didn't stop her from doing things like NaNoWriMo, being obsessively engrossed in crafting musical tragi-comedies out of Hamlet and Lear, etc. It's the quirky, sort of broad and unexpected interests that I think are the real give-away there. I mean, clearly that wasn't a list generated by parents or student either one running down some checklist of "How to Get In at Very Elite Institution."

I'd like to think that such institutions would be ALL OVER kids like mine. But the evidence seems to suggest that they often prefer the checklist-generated candidates instead.
Schrödinger's cat walks into a bar. And doesn't.