"If you want to store stuff, you would put these pits
along the bottom of the hill, not running a long distance
up the hill."
Unless you want more favorable conditions for long term storing, or in case a enemy comes and blunders what is easily avaiable at the bottom of the hill.
If you're hiding food from enemies then you're going to pack it into isolated hiding places, not jammed together with 5,000 others in a feature visible for miles around and where everyone that the enemy might decide to question knows where it is. So storage, yes, but hiding it from enemies seems unlikely.
Unless you want more favorable conditions for long term storing, or in case a enemy comes and blunders what is easily avaiable at the bottom of the hill.