And in the US, a lot of the subsidies flow towards food that isn't edible without processing - soybeans and field corn as opposed to sweet corn.

Why? Because they've always grown it. So the subsidies encourage them to keep on growing it instead of diversifying into more competitive or higher value crops.

The subsidy is received by way of reduced insurance premiums. While that does make insurance affordable where it mightn't otherwise be, the rate of reduction is the same across all crops, so the insurance is made equally affordable no matter which crop you grow. Thus, for all intents and purposes, we can completely ignore the subsidy and simply focus on the insurance as that is ultimately what you are suggesting is significant. After all, if the subsidies were taken away, all it would really mean that you theoretically couldn't afford insurance anymore and would do without.

But what is significant about insurance? Since no good discussion is complete without a car analogy, let's go there. Say you always drove a truck. By your logic, auto insurance encourages you to keep driving trucks. Which suggests that if you could no longer get auto insurance, you would start driving a bus/van/car/whatever instead. But what makes you think that? If auto insurance disappeared for some reason, why wouldn't you still keep driving trucks as opposed to buses/vans/cars/whatever? There is probably a reason why you started driving trucks in the first place that doesn't go away even if insurance did.

In the case of corn and soybeans, there is a really good reason why they are grown so much: Because that's where the market is. It is what people want to buy. They are the most competitive and highest value crops in the regions they are grown.

What subsidies?