I suspect that the corn industry actually supports the sugar price supports,as it means more high fructose corn syrup used in everything. They are 100x as powerful as the sugar lobby.
Their push for higher imported sugar tariffs and higher floor prices right now is due almost entirely to the (government-ordered, via ethanol) price increase in corn. HFCS isn't competitive @ $4.00 corn with the sugar tariff where it is now (although, to be fair, corn is limit down today, and I don't fancy corn staying at $4.00 continuously for any great period of time, absent a really bad crop some year).
Thus, increasing the already artificially high sugar price in the US is tailor-made for ADM's purposes.
That stuff will make you fat as a cow.
You are exactly right ADM & Cargill would never let this happen.