We've already talked about this though, that doesn't really fit into what you are talking about because the violence base there are based more around political identity and power and not theology.
In parts of the Middle East political structures and parties can tend to revolve around religious lines (like they can revolve around ethnic lines in say Africa), so political violence tends to also be sectarian violence much in the same way that African ethnic violence tends to be expressions of political violence.
I think the part you are insisting to ignore is that islam is a political religion. It has specific instructions on how to run a state that no other religion has in its context.
So, islam is NOT just a religion as you paint and wish it to be. It is an institution that claims power on people and the state at the same time, pretty much like the church in the mid ages.
Once you miss this nuance, of course you miss the whole point afterwards.
The problem with what you are suggesting if that, if true, all Muslims would have be be Political Islamists. They aren't though, so that rather shatters your theory there, nor do other Muslim majority countries outside of the Middle East and former Ottoman holdings have the same sort of sectarian struggles which also shatters your uniform understanding of Islam.
Once again I feel inclined to point out that Islam is bigger than your Middle Eastern understanding of it.
Islam has roots in the mid east, thats the whole problem with islam.
If you know what the mid east that gave birth to islam, it is a geography that daylight can become the darkness in minutes, because of giant sand storms. It lacks of resources (of course except oil) and all climate extremes are seen often.
When this geography produces a religion, unavoidably it is brutal.
Lack of resources, extreme nature caused by the extreme conditions of its birth place, you got yourself the greatest and most brutal violence enabler one can create. You can see the results in Syria where public beheadings are becoming more and more common.
Conflicts between people are unavoidable. But if you have a conflict with your neighbor in a westerns society, you go to court. If in Syria, you behead them.
Islam as a result of the extreme conditions still dictates its extreme on people, although human science and technology(and the greens off of oil) was able to reduce its effects on people. Arabs are living a much more confortable life than their predecessors (thanks to western tech) but because islam has a hard copy of itself unlike other religions (koran), nobody can do anything to alter the religion to fit in todays world. That's the reason you still can see imams claiming the world is flat, or that you can marry and have sex to a 9 year old, or can have 4 wives and on and on and on...
And, on top of all this, islam has the instructions on how to run the state that comes with it. So the extremes of Arab peninsula that feeds the roots of islam finds its way to government structures that are recognized as legit source of power in todays world.
Your point "why not all muslims are political islamists" is ridiculous. One can easily see the popular support for political islam all over the islamic world. If you are a politician in any of the islam countries, there is no way you will get elected to any office if you are not using islam as a tool for yourself. This is the reality of the politics of islam.
So when you look at this picture all together, islam is like the perfect storm.