Exactly. I saw a video once of an African tribe hunting in this style, and at the end the buffalo or whatever it was was just stationary in a clearing while the people walked up and stabbed it. It was literally too overheated to move anymore.

then kill them with a sharp pointy rock

In persistence hunting, at least the kind that humans practice, the prey mostly dies through indirect effects like exhaustion or heat stroke. You just keep tracking until you find a dead deer lying around basically, brought down simply by constantly having to flee your incessant pursuit again and again.