Of course it is profitable to do so. There is a large market for it, from animal feed, to sugar, to tortillas, to many things in between.

The trouble is that it's unpredictable how big the crop will be before planting. As mentioned before, yields can vary quite significantly from year to year. As such, you will have periods of excess where we don't have enough storage for it all. Ethanol was promoted as a way to clean up those excesses before they turn to waste, recapturing some of fuel that was put into its growth initially.