One important fact to add is that corn is the #1 subsidized commodity in the US, so it’s artifically inflated to being over produced. The subsidies are like 2:1 to the next most subsidized commodity.
I thought most of the corn is used for Ethanol fuel and corn for anything else would be expensive. Why sell it to someone for corn syrup when you can sell it to someone to make engine fuel?
Only about 40% is used for ethanol and that's a very recent (as in this past decade) change.
The argument you make though explains why we aren't using algae to produce biofuel. Far more valuable for other purposes as called out in this Forbes post[0]. Here's a choice quote:
> An acre of algae can produce almost 5,000 gallons of biodiesel. It does not compete with food crops for arable land or potable water and could produce over 60 billion gallons/yr that would replace all petroleum-based diesel in the U.S.