The consequence of this would be that the subsidized food gets exported to a country that doesn't tax it, at which point you're subsidizing some other country's food.

The US is also a large net exporter of food, implying there is more than enough domestic production for wartime needs. Also, the US hasn't been in that kind of a war in almost a hundred years and MAD makes it unlikely that it ever would be again. The obvious conclusion is to eliminate the subsidies.