I think your assumption that the invasion of Iraq was welcomed by its citizens is flawed.
Here is a
poll done by Time where they interviewed 1,711 Iraqis which might paint a more realistic picture.
Some extracted numbers.
60% say US & Allies have done a bad job in Iraq.
65% say they oppose US troops in the country.
Some did say things are better, but not the overwhelming positive response you were hoping for.
While their life may be improved, it is a fallacy to think that most citizens who live in dictatorships want America to invade and change the country to be more like them.