I wouldn't call them "unsustainable" because even though I disagree with the subsidies I think they're pretty easy to sustain.
But your reasoning makes no sense. You don't need subsidies to have food. Here's a study on farm subsidies that found that removing them would increase prices only slightly for most goods: https://12ft.io/proxy?q=https%3A%2F%2Fwww.agri-pulse.com%2Fa...
> The impact of premium subsidies – which work as discounts on the amount that farmers pay for crop insurance - varies widely depending on the crop and the policy. The price of corn, which is primarily used for livestock feed, would rise by nearly 5 percent if the subsidy were withdrawn, which would hurt livestock operations as well as foreign customers and ethanol producers.
> Lusk says that removing subsidies would lead to at least small price increases for all foods, with the largest increase, of 1 percent, for eggs. Meat prices would be about 0.55 percent higher. Fruit and vegetable growers also benefit from the insurance, so prices for those crops would rise by 0.67 percent, Lusk found. The price of dairy products would be 0.14 percent higher.