If your "strategy" is to prolong the fighting, widen the conflict and drag the US into another regional war maybe... otherwise it looks like more globalist intervention that the American people are sick and tired of.
If we don't stay then sooner or late the Iranians and Russia will control the area and cut-off the Straits of Hormuz to attack the Saudis and Gulf States.
Oil will move to $200 or more per barrel and gasoline will be $10/gallon or more in the US, if you can get it at all. Our economy will crash, and the impoverished voters will probably vote for some socialist.
Could we make ourselves independent from what happens in various Middle Eastern sh*tholes? Sure, but the likelihood of that happening are about the same as death by meteorite.
If we leave the ME now, we'll just be back again in an even worse situation a few years from now or have an even bigger war somewhere else as a consequence of our defeat. Non-interventionism is a political fantasy. And right now we are maintaining an important strategic position at almost no cost, so it would be even more stupid to throw it away in a fit of pique.