Turkey does not get along well with the PKK- who does not get along with the Peshmerga - sound like a familiar Arabic proverb?
The US did not have to go into all of Iraq. They could have taken the oil fields, air - no fly zone over Iraq and waited for them to turn over who they wanted.
Set the Kurds up in their own state. recognize them and others would as well.
The let the Sunni- Shia form their own states.
Iraq is a failed state, an artificial state since after WW1.
With long term US Base leases.
Right on top of the Stans, with oil/gas lines-fields, and Iran close.
Putin would have had a heart attack.