Attacking through Turkey would have made little difference. Our problems in Iraq were/are not rooted in the axes used during the kinetic/manuever phase. The Iraqi security forces still would have been disbanded/ignored, the tribal leaders still would have been marginalized, the water and electricity still would not have been turned back on, and we still would have reached a point where we faced insurgent momentum with too few boots on the ground.

The PKK have rarely been so foolish as to attack US forces or USG elements. IMO, they would not have started doing so with a division rolling through their front yard. Besides, there are segments of the Turkish military-industrial complex that benefit from the continued existence of the PKK, in the vacuum created by the demise of the Cold War.

Cheers,