Temporarily, perhaps. But historically the American farmer has ALWAYS overproduced sufficiently to drive prices down, even in the face of seeming insurmountable demand.
Yes, what’s the old saying, nothing cures a high price like a high price. Producers will produce more to capture the higher prices before consumers cut back, then the prices will drop as demand decreases. It all works as long as there is some elasticity in supply and demand, and minimal “tinkering” by non-market forces. At least that’s the theory as I learned it.