Makes all the difference. It's not yours, not even in the "we're all part of the government" sense. Ownership means something.
And, FYI, you seem unaware of modern supply chain management: darn near everything operates on a "just in time delivery" model. Even food, if you'll look close at where it comes from: if some food is in season, it's sent to where the demand is now; to significant degree it's cheaper to ship food around the world for use ASAP, than to store it in giant refrigerators waiting for local demand to catch up with warehoused supply. Yes, there are lots of giant refrigerators holding lots of food; that food doesn't stay in there long before being removed, used, and replaced.
And as you note, Agribusiness as a whole is oriented to a “push” system by which farmers sell to commodities brokers, who in turn sell to retailers, very carefully calculating market demand ahead of time, so that farmers do not over or under produce. Black swan events, like massive national rioting, is not included in those careful calculations.
“just in time delivery” is a more accurate way of describing “push”. However, this being said, the end result is a paradox.
Private ownership does indeed mean that goods flow to where they are most profitable. However, government ownership implies rationing not based on market forces. Neither are good as extremes, but both can function in parallel to better result.
In this case, if there is a national need, there are many ways government can restrict exports. Likewise (like with sugar), if there is strong national and international competition, government can restrict imports.
But in exchange, government can only efficiently ration to the neediest, based on what the public wants to provide to them. They are, however, effectively outside of the market in this process.