As you say it was stable under the Ottoman empire, because they took over and kept it, America needs to do the same thing. The US, Canada, Australia, NZ were all British colonies, but the difference is the white people never left, so they remain beacons of progress. Hate to sound all racist here, but there is a strong correlation between those and African, Middle Eastern states that were given back.
I think you should probably read a good history of the British empire, followed by 20th century history, before posting nonsense like this.
The causes of problems in the middle east have a lot to do with the long term history of the "beacons of progress" fucking with the region. Specifically when the Ottoman Empire collapsed the colonialists divided the region up along entirely arbitrary borders that often drew straight lines right through native tribes and populations, then appointed flunkies to rule these new countries. There was zero attempt to make something that worked for the people who lived there. This caused serious long term resentment.
Have you ever watched the ISIS video of them blowing up border posts? The ISIS soldiers keep talking about the end of Sykes-Picot. Even though I actually have read a history of the British Empire, I still had to look that one up. It turns out to be the British-French treaty that created the borders of Iraq. Families in different villages were suddenly divided from each other, etc. The people who live there apparently still hate Sykes-Picot to this day.
Plus, when countries in the region got leaders the western powers didn't like, there were interventions (e.g. Iran). There were invasions. Not to mention the gaping wound that is Israel and the absolutist support for it from the US.
There hasn't ever really been a time when more powerful militaries weren't fucking with people who live in the middle east. Religion certainly plays a part, but the USA is a lot more religious than other western developed countries and it doesn't seem to hurt them much