I would argue that the reason is less political and more about geography and economics.
As this study shows, access to low-cost fossil fuels is in fact cheaper than nuclear. This page shows the cost of fossil fuels to be reasonable, whereas nuclear has a high capitalization that must be amortized in some fashion.
Saudi Arabia, for example, has the world's largest oil reserves, and thus can extract oil far more cheaply than they could invest in such a large scale infrastructure project like a nuclear power plant. Egypt, Syria, Algeria, Libya, and others likewise lack an economic incentive to do this.
Iran's nuclear program is more contentious. While Iran claims it is simply diversifying its energy portfolio, many in the West view it strictly as a ploy to cover a nuclear weapons program - not as an energy source.
Israel, in contrast (a non-Arab state), has no oil reserves of its own, and a precarious geopolitical situation that makes it prudent not to rely on its neighbors, and sufficient wealth - but even in these circumstances, has found it cheaper to emphasize solar power and conservation.
And finally, some countries, like Germany and Japan, in light of the externalities imposed by the cleanup of spent nuclear waste, have seen fit to actually dismantle their programs. While the price may have been affordable, the total cost, both environmental and political, was deemed otherwise.