Isn’t your “cheese” analogy exactly how the mouse meets his fate?
The only way, is to eliminate the free cheese.
There is a factual history of early America which deals with just that idea.
A reading of Governor Bradford's diary of the experience of the Jamestown Colony might be instructive here. After the near starvation of the early Jamestown settlers under a communal production and distribution system, where all were fed from a common storehouse of goods, whether they worked or not, Governor Bradford's diary gives account of how all benefited after agreement that each family could do as it wished with the fruits of its own labors
He reported that all became more industrious, and the hunger for "free cheese" (your term, not his) disappeared--as all had plenty.
America's Founders preferred liberty for individuals, and their principles made America a desired destination for millions for over 200 years.
"To preserve [the] independence [of the people,] we must not let our rulers load us with perpetual debt. We must make our election between economy and liberty, or profusion and servitude. If we run into such debts as that we must be taxed in our meat and in our drink, in our necessaries and our comforts, in our labors and our amusements, for our callings and our creeds, as the people of England are, our people, like them, must come to labor sixteen hours in the twenty-four, give the earnings of fifteen of these to the government for their debts and daily expenses, and the sixteenth being insufficient to afford us bread, we must live, as they now do, on oatmeal and potatoes, have no time to think, no means of calling the mismanagers to account, but be glad to obtain subsistence by hiring ourselves to rivet their chains on the necks of our fellow-sufferers." --Thomas Jefferson to Samuel Kercheval, 1816. ME 15:39
"Were we directed from Washington when to sow and when to reap, we should soon want bread." --Thomas Jefferson: Autobiography, 1821. ME 1:122