As the Aquatic ape (my other favorite theory), the Endurance hunter theory is sexy because it give one simple logical explanation for a lot of various traits. I guess Humans are addicted to simplification
The arguments for the persistent hunter, is one of accumulation based on a presupposition: We have hair, it protect from the sun while we run. We sweat, it help cooling for the run. We are bipedal, it's for running. We experience a runner's high with endorphin kicking in after 5 miles.. comon, of course we evolved to be persistent hunter
The one argument again persistent hunter is the diet.
Long Running need a lot of carbs. Even if you catch the prey, you get protein and some fat, but you cant replenish those carbs. And if you don't catch it, like it apparently happen a lot with the Tarahumara people (on a side note, the one and only primitive tribe using the persistent running technique) you're exhausted, with nothing to show for your effort, far from home, and you'll likely become the prey of the nasties around. Not very smart
Tarahumara live on a high carb diet75-80% of their diet are carbs.. not many protein( yeah they are bad at hunting prey). Such diet is only possible with agriculture
Basically we need agriculture to persistent hunt, which defeat the purpose