Not so. Many of the Islamic sultanates have existed for over a thousand years. There were centuries if relative stability after the Ottomans consolidated the Byzantine Empire. I say "relative" as Europe was often in a more chaotic state than the Middle East for much of its history.
Yes, and Islamic nations occupy near a third the earth's landmass including strategically vital waterways and shipping lanes. Furthermore, the modern world and the traditional Islamic societies are on a sort of collision path; globalisation, international trade and relations and so forth, ensure we cannot avoid involvement. But the real problem of course is the hostility and belligerent actions of Muslims whether on a nation state level; irredentism, menacing Israel and the West, or on a smaller level with groups, often tribal, waging a war of terror against the non-Islamic world.
Given the fact that the United States is the only thing preventing a major world war breaking out and given the realities of globalisation in the 21st Century we can't really "leave" the area and even if we did our embassies would be bombed and shipping lanes attacked, allies menaced and invaded - in short, it would be a catastrophe. The US needs "forward operating bases" in these places in order to protect our national security. Surely?
And we've had relative stability from the royal families of the region in comparison to the alternatives that have presented themselves; military dictatorship, secular/quasi-religious tyrannies like Saddam, Gaddafi, Assad etc.