I have a theory on the history of humans that I would like to share. I do not believe that early humans started out hunting animals. I bet when they wanted meat, they would steal it from predators that were better at hunting animals. I mean, sure, its hard to scare off a lion and eat its dead gazelle, but that is a lot easier than for some guy to catch a gazelle. Or even take down a gazelle with a rock or a spear. If it was me, I would use that rock or spear to chase off or kill a lion and steal its food. With a friend or two, and using rudimentary communication, no big problem; kind of how hyenas steal food from the big cats. In fact, I bet the first domesticated dogs were not just for companionship, but to help harass big cats to steal their kills.

And that is why early humans would need to cook food. A freshly and personally killed animal would be fine to eat raw, but a kill that was stolen from another predator might already be a few days old.