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.
You forgot about the height. It will overshadow the smaller crop, and lack of sunlight on this smaller crop may simply not produce any ears as a result. Just a "balcony farmer" but that is what i have seen with most plants that are overshadowed by dense/taller plants.
A good story that touches on this is the Wizard and the Prophet, covering Norman Borlaug's efforts to crossbreed wheat that wasn't too tall, was resistant to blight, etc.
That reminds me, I never got back my copy of that book...
That’s true in generation 1, but breeding isn’t a single generation. You repeat things across generations until you find a stable mix.
You just raise the head.
You harvest the top crop, the one you want, cutting above the lower height, then go back through and make a second pass with the head lower.
You'll lose some of the lower crop, crushed under the wheels, but it was there as bonus anyway.