Except that it’s the insulin response that causes the body to put away fat. And repeated insulin responses do cause some people (or most, actually) to become insulin resistant. Pancreas produces more insulin to make up for it, which takes longer to flush out and makes muscle and organ tissue cannibalize itself because it can’t access the fat stores in the body. Eventually, many people get to the point where their body just has a constant supply of insulin pumping through their bloodstream, which means that any calories beyond ones that can be burned in the next couple of hours are going to be put in fat stores.
OTOH, when people consume too many calories without the insulin response (or without the insulin resistant insulin response), what happens is their bodies up their resting metabolic rate in order to burn through those extra calories.
