Depending on the expense of making the new material, it may become actually feasible to build solar panels across Sahara and feed both Africa and Europe with the electricity generated, because transmission will become lossless and physically compact.
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