It was a high cost, and US soldiers and policy-makers were captive to Iran and their Shiite allies who could attack or make trouble at will. But Bush did achieve a measure of stability, which Obama, out of spite really, just gave away. The US would have needed to stay in Iraq for 50 years or more to achieve long-lasting peace. If that's the case, we should have just nationalized their oil industry to pay for it all. its what the Romans were forced to do when dealing with uncivilized nations they took over.
I agree when you say “stay,” but we have “stayed” in Germany for 70 years. We would have had some bases there, and indeed SHOULD have taken some of their oil for payment in a “treaty.”
I’m still mystified, as a historian, that we are apparently the only nation on earth to win a war (Mexican War) and PAY the loser.