“Butch Cassidy and the Sundance Kid” suggest that criminal gangs in the Old West opperated that way. “The Virginian” suggests something similar about the way a foreman works with his crew. As does perhaps “The Hairy Ape”, Eugene O Neill’s 1922 story of the manufacturing industry.
Ia contrast, C. S. Forester says the opposite about the British Navy: challenging a superior officer to a duel is a hanging offence.
The idea would only work at the top.
First, the boss does not want others making decisions for him. He alone gets to decide who advances and does not, in an authoritarian state. Besides, like any other society, open season on its members for whatever reason is counter-productive. Superiors may have some degree of control over their subordinates, but again, allowing an intermediate authority power of life or death over his subordinates also invites chaos, and runs the risk of creating lethal blood feuds… which again is chaos, something a society cannot really tolerate.
Even the most vicious societies tended to have some pretext of legitimacy for acts like executions.
Plus, as mentioned, the other problem is that for self-protection the higher-ups would deliberately sabotage or murder their subordinates if they see them getting too powerful. this was an additional problem in the Roman Empire and the eastern empires - a general who appeared too powerful or too well liked would be sidelined either politically or permanently. but, this was very much like shooting yourself in the foot.
For example, Henry VII and his son Henry VIII were well aware how tenuous the Tudors’ claim to the throne was; VIII spent a lot of time persecuting and prosecuting any potential rival claimants. The problem was not always that these rivals might challenge him, but also that they could be promoted as figureheads by an ambitious but genetically unqualified claimant. Better to avoid having rallying points wandering around the kingdom. (And when his son Edward died, a faction tried to promote Lady Jane Grey as a figurehead Queen based on her pedigree - so she got her head removed).
What’s so special about Arab countries? Heck, for all I know, all Western countries have been playing that game for hundreds of years!