Another version of the starvation objection to this hypothetical is this:

Such a system would rather quickly result in large groups of people inventing ownership and protecting it by force, by threat of violence. Maybe not the first time the half-ripe tomato you don't own but which you planted is eaten by someone else before you eat it you will not sign on to this alternative. But if you manage to stay alive long enough, you will soon be trading your labor for food and be incredibly grateful that the same system which is LETTING you trade your labor for food is also setting up powerful violent incentives for others to leave you in peace with "your" food.

This is a version of my own "objection" to anarchism. Anarchy is unstable to the formation of what is, effectively, government, and the essence of government is a system that tells you what is NOT yours, what is yours, and provides powerful and violent responses to those who "disagree" with their characterization. If you are lucky, you get the American constitution, if you are half-lucky you get the Mafia in 19th and 20th century Sicily, and if your luck is lousy you get roving militias in Toyota pick-up trucks with machine guns mounted in the back.

I await your counterfactual proposal on how to prevent the formation of a government or a militia.