The area has become an American vital interest and the power disparity is just too great. Sure we have our share of incompetent idiots - it is still foolish to just stand there when the blind giant is stomping around. Turkey had its chance at controlling northern Iraq and blew it.
American forces will move into northern Iraq from the south. Turkish forces in Iraq will then either make themselves useful on American terms without compensation or face the consequences. The goodwill necessary to minimize unfortunate incidents won't exist.
Yes it will be tragic, and should have been avoided. But it will happen on Turkey's doorstep and not ours.