The idea that the US can legitimately use its military power to ensure continued access to oil resources rests, in large measure, on the (not entirely unfounded) assumption that those controlling the resources are a bunch of sheikhs and military adventurers who happened to be in the right place, with guns, at the right time. Without the Arab exception, the idea of oil as a special case, not subject to the ordinary assumption that resources are the property of the people in whose country they are found, will also be hard to sustain.
Certainly if you were just to look at things in coldly rational terms, the resource-rich country the US should be seeking to dominate militarily is Canada, located conveniently next door. And, indeed, in the first half of the nineteenth century that’s how hawkish American politicians saw things. But it would be politically unacceptable in a modern context to try to bully Canada or Norway into coughing up oil.