There are documentaries of wolves and wild dogs hunting large prey by chasing them until the large prey is so exhausted and overheated that it collapses.
The only people who persistence hunt still are the people who didn't find a better approach. Be it that they don't need a better approach (which is fine. Means they're optimized) or that they simply spend.so much time hunting that they don't have the excess time and resources to experiment with new approaches
I also think it depends on the environment. I can imagine ancient humans persistence hunting across the plains of Africa. I have a harder time picturing it in rain forests or the forests that used to cover most of Europe.
Arguably dead weight ballast scaled to the same fraction of total weight would be more fair than unburdened runner vs horse+rider, but if you expect the human to carry another human (but not the horse to carry the equivalent of another horse) you might just as well go full symmetry and require the human to carry a horse. In this variation, horse would lose to elephant.
https://en.wikipedia.org/wiki/Persistence_hunting
There are documentaries of wolves and wild dogs hunting large prey by chasing them until the large prey is so exhausted and overheated that it collapses.