This is a great practical approach, but when you harvest the crop you get a mix of higher crop and lower crop. It is more difficult to sell some mix than a pure crop with known properties. Technically, it would be possible to build a harvester with two cutters at different heights to separate the crops, but I've never seen one.

It seems like the genes that cause long stalks also have other benefits, otherwise they'd have been bred out a long time ago. At least that is what I figure.