True. If the military had gone in on day one and started blowing away looters, we'd have a different story line from the Left: Fascist Bush Sends Soldiers to Kill Oppress Blacks.
IMO that would have had less traction than the current meme. Americans wanted order out of the chaos. This was one instance where Bush could have been the "dictator" his enemies imagine and gotten away with it.
You overlook one very important point, though. The military would have been blamed for every bullet-riddled body that emerges from the murky waters of New Orleans even if the military personnel didn't carry any guns.