Hunger is a solved problem everywhere there is a free market.

It makes sense for countries to protect their domestic food production as a military asset - cutting off the food supply is a common warfare tactic. Subsidies also come about because of powerful agricultural lobbying interests. As to if subsidies reduce hunger, the evidence is scant to none. There is plenty of evidence, however, that they result in inefficient misallocation of resources, such as water.

Also, many subsidies in the US are in the form of price supports, and paying farmers to not farm. These are designed to increase costs to consumers, because the free market was allegedly too successful in reducing the price of food.

Check out the great American pig slaughter during the Depression:

https://livinghistoryfarm.org/farminginthe30s/crops_17.html

The subsidies are actually minuscule, compared to welfare spending and other transfer payments to the needy.