“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.
(Banging head on wall.)
In EVERY CASE in history, when govt intervenes to “smooth out” the food and medicine delivery, get it to “the needy,” and apply cost and export controls “for the common good,” shortages are the nearly immediate result, leading to worse rationing, worse mal-investment, worse shortages, black markets, etc.
Picture Cuba, Venezuela etc.
Which brings us back to the unanswered question: where are these well-stocked government food warehouses?
Answer: there aren't any for a scenario of this scale; the government just buys what it needs from the private "just in time" supply chain which only has enough for short-term non-crisis situations.