Well CarolC I suspect you are correct in that they may have wanted a battlefield away from home, they have accomplished that one.
I disagree with your judgement that they had the power to prosecute the war in a different way. Their intelligence agents failed miserably with human intel gathering; and the over reliance on high tech stuff was in many ways an arrogance born of stupidity. I still think Bush was fed a diet of bad information; and I have to say I saw nothing in his planning that wasnt born of genuine shock and revulsion to 911.

Nuturing democracy in the Middle East brings to mind the old prose by Kipling..."A Fool lies here who tried to hustle the East." I doubt if it is possible in our lifetime to change the way these countries exist. Several hundred years of induced ignorance, poverty and resistance to change will not be easily wiped out. There is always hope that education and the desire to live a better life will encourage the Middle East to adopt democracy. Opening the door to education and equality for women would be a good start. But like Kipling said:-
And the end of the fight is a tombstone white with the name of the late deceased, And the epitaph drear: "A Fool lies here who tried to hustle the East."

there will be a lot more tombstones before we see the end.