Even bison will run away from you, and they'll outrun anyone both in terms of speed and distance.
Persistence hunting works in very particular topography and climate, and no where else. You need it to be very hot, or I suppose very cold. You need to be hunting on a vast, open landscape where it's easy to track your prey and where it can't hide. Persistence hunting wouldn't work in most temperate regions except in the winter, and even then you need an open area where the animal can't just hide. Persistence hunting would be impossible in a forest, regardless of the temperature. Trust me, I've tried it.
What I was getting at with my first post is that hunting with spears is an art that requires the hunter to learn stealth and master ambush. I've gotten within grabbing distance of deer, and that's the distance you need for spear hunting, whether throwing or thrusting.
Throwing spears is challenging, because it's a big motion and deer jump at everything, so you're almost guaranteed to miss unless you catch it completely by surprise and it doesn't see you throw the spear. You also need space to throw, and the places that will hide you enough so that you can get close usually don't afford the space needed for a smooth throw. Unless you climb a tree. Many First Nation tribes carried spears, but I think those were more weapons to use against opposing tribesmen than hunting tools.
Thrusting, in my view, is easier because you can position yourself where a relatively small motion will put the spear tip in the animal's side. With a thrusting spear the idea is to impale the animal, tackle it and pin it to the ground until it dies. I suppose on something larger you might have to jump back and let it run off and die, then track it down once it's expired. Or spear it and back off, and pray it doesn't attack you as even herbivores will attack when wounded at close range.
I have an acquaintance who killed a fawn deer with a thrusting spear maybe six years ago. It turned on him and kicked him in the chest with one of its front hoofs. It hurt so bad he thought it had broken ribs, and he felt his heart beat irregularly for a few minutes before it regained its normal, consistent rhythm. It turned out that his ribs were just severely bruised, though. He says it was a harrowing experience, and he doesn't plan on doing it again. And that was just a fawn. Imagine going after an adult! Or a bison!