> The primary subsidy afforded to farmers is effectively assistance in paying insurance premiums.But the vast majority of the subsidy goes not to small individual farmers, who might need such insurance (although even on the assumption that they do, private sector insurance companies and speculators could provide it more efficiently than the government does), but to large agribusinesses who have more than enough resources and diversity to self-insure. So the entities who are getting the subsidy don't actually need it. But it makes a great way for politicians to stealthily transfer wealth to their donors and supporters.
> The intent is not to make food cheaper (although that may happen as a side effect)
It doesn't make food cheaper, it makes it more expensive and creates a mismatch between supply and demand.
> I am not sure that really limits the desire of innovators and entrepreneurs to seek out ways to provide cheaper food.
It might not limit the desire, but it certainly limits the ability. It's hard to compete with large businesses that get government subsidies they don't actually need.