So at that point, our military in the ME are targets. Without the aid of Iraqi military, troops in Iraq could just get picked off here and there - no place off base would be safe (even the bases wouldn't be safe - can incoming missles can be fended off with 100% certainty?). If China were in Canada, initially with Canada's approval, and Canada subsequently told them to leave, and Chicoms refused, would we blame Canadians for engaging in guerrilla tactics against the occupying Chicoms? Would we blame Americans who went over the border to help Canada?
Having our military in countries where we aren't wanted just leaves us sitting ducks - for justifiable attacks by patriotic Iraqis, their Iranian allies, or for a Mossad false flag (because Israel would love for us to go to war with Iran - which of course is why American neocons have had Iran on the short list for decades).
There is no winning for America here. Bring our troops home, and defend our own borders.