I think what really got the press going was the very visual presentation of Rumsfeld saying, and I remember seeing it and as an archaeology buff being incensed myself, “What’s a few broken pots,” regarding museum destruction or the like.
The Bush administration did a great job of successfully conducting the war, but had made no provisions for preserving or protecting world heritage items or sites. They had been repeatedly warned and urged by archaeology professionals that this was important to do. We owned that war and had the power to do something about that. ISIL/Daesh has possession of some important historic territory. Bombing into the stone age might kill ISIL/Daesh, but also can destroy as much or more than they have already destroyed. A really hard choice.
Uh, the looting of the museum was very minor; the really high-end stuff that trumpeted as having been boosted while US troops and the President were supposedly high-fiving turned out to have been locked up by museum staff at the first sign of trouble, and that where it remained.