Why is it faster to reheat something than it is to cook it?
"Cooking" is often a chemical process.  Denaturing proteins, gelatinization, causing chemical reactions like browning, or even causing state changes like evaporation.

In many cases for these reactions to happen, we need to overheat the food.  (Cook it and let it rest to cool off back down to undo some of the changes that were made and/or bring it back down to a reasonable temperature to eat).  This is true when grilling meats, frying, baking bread, and lots of other types of cooking.

Other times, we need to bring something to temperature and hold it there for some period of time.  This holds for extracting collagen, starch gelatinization (eg, cooking pasta, potatoes, etc.) but also just waiting for flavors to transfer in soups and similar dishes.

With warming, you're just adding enough heat to it to move it a few degrees, but you're not typically trying to change the state of the food, so less total energy is needed.

Now, it is always faster to reheat vs. cook things?  For the most part it's true, but I suspect that there would be an edge case out there.  Something that's cooked from room temperature, but then stored chilled and the chilling causes issues (like retrogradation in starches, maybe?) that make them more resist than reheating.