Let's open an history book an review what happens when the government controlls the food production.
I would say this is simply wrong. Government often capture food production and use it to enrich themselves. Some historical places certainty had a function in distribution as well but this is not the common case.
The waste majority of history, government were primary involved in food production and distribution beyond capturing as much as possible and distribution it to its own armies.
Most of history food for the most part was produced and consumed fairly locally without much involvement of government.