At the time it was started, the war was over refusal on the part of Saddam to "open his house" to inspection. He was in violation of numerous UN orders.
The other positive attributes to regime change (more transparent government, government answerable to the people via elections) naturally tag along, and would hold in many countries. Zimbabwe would be better off with regime change, as would N. Korea, Somalia, Iran, Cuba, etc.
No, you are wrong. All those things that you mentioned were tag alongs for the establishment of a viable Islamic Democracy which President Bush felt was the essential tactic in the war against terrorism. Bush considered all those things that you mentioned as further reasons to sell the war to the congress because he did not think that they would fully understand and support going to war to establish a beach head for Democracy in the center of the Middle East. That's where the WMDs came in, as an over simplification.