The tenth man or devil's advocate's purpose is to be a contrarian to test any ideas, theories, concepts or assessments against falsification thus insuring these are either proven correct or shows that they must be either modified or discarded as incorrect. This is not to say the devil's advocate is always correct or never correct or the percentage of accuracy is necessarily the goal as the purpose is to question consensus to force its advocates to defend their position and prove it correct.
It is then necessary for the devil's advocate, in order to be effective, needs to be somewhat above average intelligence and be self-sufficient enough to not feel the need to be part of a group and to be able to consciously stand outside the group. The tenth man would have to be very much of an individualist and smart enough to hold his own as such.
I would submit that the Israelis noticed a certain type of personality trait, realized its utility, and simply formalized it as a methodology under the devil's advocate or tenth man concept.
Here I must emphasize that this is purely a speculative hypothesis based on my own observations and information that I have read. At this time, I have reason to believe I am correct in this but it may be that later on, I will come across new information that would negate this theory which I would then discard. So stay tuned.
I would postulate that this tenth man sigma type was through our evolution as hunter-gatherers, for one a check against mistakes in group think that would be potentially disastrous for the tribe. He would be more individualistic and prone to think differently than the group, curious about things the group may consider irrelevant or inconsequential. This would lead to a certain inventiveness and innovation, the primary driver of technological evolution that would benefit the tribe.
Perhaps that one time the devil's advocate would be right about the chief's bad decision, or be crazy enough to pick up a burning stick, invent the wheel or fashion a better spear tip would make up for all the other tumult and aggravation he would otherwise cause to the alpha male chief and make him worth keeping in the tribe. This allowed him to mate and pass his genes on to latter generations.
But the tribe could only afford one such type otherwise it would dissolve into pandemonium or simply stretch the patience of chief and tribe to the breaking point. So most likely, they would only keep the smarter one, the one crazy enough to pick up the burning stick, use it to chase away predators, then put it on the ground, use it to cook meat, and keep the tribe warm. The one who could at least be sometimes useful. The rest, well...
Expanding on this, it would also conform with my theory from an earlier post that the original ethnic Americans of the colonial era had a much higher than average percentage of these tenth man/sigma type people. Look at the tumult of the revolutionary war and early in U.S. history with the Articles of Confederation, Shays' rebellion and later the civil war for a brief example. This is counterbalanced by the inventiveness of individualism characteristic of American "git 'er done" ingenuity. But the tenth man/devil's advocate/sigma type was gradually diluted to their near normal percentage of the population through later waves of immigration.
So it seems that despite the frustrations to alpha leaders and the peasant masses the tenth man can cause, the American example would demonstrate that it is possible for devil's advocates en masse and at times to agree on an overall goal and cooperate in achieving it. Just because someone prefers to stand outside the group, it doesn't mean that he is a complete sociopath that has no interest in, or would not identify with the group or have no stake in the group's success. He just asks too many inconvenient questions of the leaders to their chagrin and challenges the leader's assumptions. A nuisance but a necessary and useful one. We could use a lot more of them today.