Maybe it could be a stabilizing factor, because the many interests involved would be mostly aligned. However unstable Middle East is, most of the time no oil well is on fire, or in a war zone.
It is not about the steady state being unstable on its own, it is about how easily it can be brought out of equilibrium with a very small force (of a hand full of people). An inherent flaw in the centralized nature of such a system
