Three thoughts:
1) Lots of Ivy League KIAs in Vietnam.
2) Never saw a rich punk beating the drum for war. The rich punks I knew were beating the drum for peace, love, and Communism.
3) Being a veteran seems to increase your maturity and also your employability. It teaches discipline and responsibility, and employers (and potential fathers-in-law) value that. That's why non-Ivy type kids willingly join up. Several of our home-school group boys are in the Marines, one in the Coast Guard. When they're home on leave, man can you see the difference.
The ivy’s im sure had a few. But they weren’t exactly the soldier factories you imply. And today ivy participation is nearly unknown. But the ivy’s do contribute most of our red white and blue national leaders... who often excitedly point the cannon at you.