The Paleo diet is geared to a MUCH different lifestyle than any but a very small handful of humanity now enjoy, if “enjoy” is the word.
It was often “feast or famine” for paleolithic mankind, and certainly, what is claimed to be the “authentic” Paleo diet missed by quite a few spoonfuls. For one thing, in extreme famine, the consumption of grubs and crickets became something of a staple, as well as simply swallowing handfuls of dirt. Also, regular meal times were highly unlikely, with what we consider to be “grazing” a much more common dietary intake pattern, or even eating only once in perhaps a couple or three days.
The fact is, people are really overthinking this “recreation” of the “Paleo diet”. Pretty much like a hog out rooting around, you ate what you found.
Your point that paleo people did not have constant access to food is a valid one. But your conclusion is not. Intermittent fasting, and irregular eating patterns, are a hallmark of the paleo/primal approach.