If you found yourself in a situation where getting food or shelter now was a matter of life and death, and you effectively had only one supplier, it would. But you usually have time to find alternatives, and usually can skip the shelter altogether, and the markets are so large that it's usually hard for a supplier to form a monopoly or a few to form oligopoly.

On top of that, even "pay-up-or-die" doesn't mean that the price will be a billion dollars. Instead, it means that it's the price that maximizes total profits. Suppose that no one could ever pay more than $30,000 for the medical helicopter. Then the helicopter people would set a price that prompts people to pay as close to $30,000 as they can. Perhaps if patients see a bill for $50,000 they negotiate down to $30,000, but if they see $500,000, they go to court and only at the end pay $30,000. Similar dynamics can limit food prices in areas that really only have one food supplier - there's only so much you can charge, and if you charge more than that, you won't succeed in squeezing more out of them, but you may attract all kinds of trouble - violence, or legislation, or competitors, etc.