Germany, South Korea, and Japan. If we could help rebuild and reform two of the nations that helped start WW2, I think America has earned the right to say our presence has a stabilizing factor, considering all 3 of those nations are among the wealthiest in the world today.
Germany and Japan were already world powers before US bombs fell on them... We are not talking about some third world desert...
And Germany and Japan did many things to educate their people against war, that's why they haven't still invaded anybody. It's not because US troops are in their country.
It truly has nothing in common with what you did in Iraq. During the WW2, the USA came to liberate Europe against the Nazis aggressors, and everybody, including the Germans, saw what the Nazis did. Germans, except the hardcore SS, had less reasons to be angry at you (well there are still the carpet bombings over the cities...). Well in Japan, you were under attack and you defended yourself. It's ok. And with the weird Asian pride, you managed to take profit of it.
Now, in Iraq, you are the aggressor, you attacked a country under the account they had WMDs, without any evidence except the usual lies USA love to use for their false flag operations (Tonkin incident for example). Don't expect people to believe in you on this matter. If the US troops stay 100 years on Iraqi soil, it'll be seen as 100 years of occupation like Germany in 1940 France. Hatred all over from all the muslim countries, as usual.