Bush II did do that, unfortunately he chose the arrogant and inept Paul Bremer to be the head administrator. I don't think Bremer made a correct decision the entire time he was there. And that's on Bush as well as on Bremer.
But your point about Japan and Germany is very well taken. It is worth noting that in both those cases the administrators were competent military folks.
Letting Iraqis wander the streets with weapons, and giving them a say isn’t imposing an administration. Any and I mean ANY Iraqi with a weapon should have been shot on sight.