Why couldn’t something that says “Cook at 400 degrees for 15 minutes” theoretically be cooked at 6000 degrees for 1 minute?
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Lots of good explanations here. Essentially we usually want to make sure something cooks through without burning on the outside, and thermal transfer takes time. Most baking temps top out around 450F, except commercial pizza ovens, which can be as hot as 1000F and do bake a pizza in literally one or two minutes. That works because pizzas are flat and thin, and cook through quickly.
Just adding that smaller changes in time/temp are used deliberately by cooks and bakers all of the time. It’s common for muffin recipes to have the first 10 minutes of cook time at 50 F higher to activate the baking powder and make them rise quickly. Then the oven gets turned down to make sure they bake through without burning. Likewise it’s common to sear meat at high heat in a pan and then put it in the oven at a lower temp to cook through.
But there are actually lots of examples of the opposite of your question–cooking something longer at a lower temp. Immersion cooking (sous vide) uses pretty low temps (less than 200F) and can hold a protein at that temp for hours without overcooking. A crock pot or slow cooker also uses this “low and slow” method.
Time and temperature are not equal parts of the equation. If you subject something to the surface temperature of the sun for a minute, it will not turn out well done. This is because the surrounding molecules are moving that incredibly quickly that your cake or whatever would burn to a crisp.
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