I really don't think whether the prey is big-game or not matters with respect to "spoiled" meat, however, contra to what some others here are saying, persistence hunting is (or was) a real thing. This paper [1] describes ethnographic examples of persistence hunting; heck, my grandfather described to me running down rabbits as a way of hunting them.

However, I would also argue that a more common approach, at least when there are multiple hunters working together, is to "herd" animals into kill zones such as pit traps, or channels. We have lots of evidence of those in the archeological record, such as here [2] and here [3].

I actually suspect that bacterial "preprocessing" of meat would assist in digestion. Rather famously, it is hard to get everything you need in a raw food diet, and a well known argument in anthropology is that cooking with fire is our way to make food easier to digest (rather than approach the problem the way, say, cows do). Fermentation can also improve the digestibility of foods (increasing bioavailability of calories, nutrients, etc.).

[1] https://www.journals.uchicago.edu/doi/10.1086/508695 [2] https://albertashistoricplaces.com/2018/07/18/pronghorn-trap... [3] https://torbygjordet.com/food/hunting/