"The 'mess' is something more than this divide alone."
That's a fair point. If we think of what might cause "Middle Eastern instability" in terms of a pie chart, then there's definitely slices of that which would belong to Israel, oil, and other Western/foreign impositions (by the way, let's not forget Russia's historical role in stoking Middle East conflicts, whether or not we consider it a part of the "West"). My point is that, at least since 2011, and I would argue even earlier (when Iraq began falling apart in 2004/2005), the Sunni-Shia divide (and other smaller sectarian conflicts, like tribalism in Libya) have become the *predominant* driver of Middle Eastern conflict. Given that these conflicts have resulted in *hundreds* of thousands of deaths, I would trace at least 90% of today's Middle Eastern conflict to this source.
I say this because the Iraqi Civil War (which is, in my mind, a more precise description of the conflict known more commonly as the "Iraq War") and the Syrian Civil War have unleashed bloodshed orders of magnitude larger than the Israel/Palestine conflict, or 9/11, or yesterday's Paris attacks. It's unquestionable that, as Western observers, we are more sensitive to the role the West has played historically in the Middle East as well as the attacks on Western soil. It is also comforting, in a way, to believe that the tools to stop the bloodshed are available to the West, if only we had the right policies. But that Western-orientedness distorts the larger reality of what is happening in the Middle East.