There was plenty of anarchy, corruption and chaos in Germany, especially in the early days under the occupation armies. The Brits and French forces were feared as rapists and with good reason, and don't even ask about the Russians. The reputation of the Americans was they were prodigious drinkers and could be seen in the mornings passed out under bushes along the roadsides. But they also loaded up deuce-and-a-halfs with frauleins at gunpoint on Friday nights and dumped them back home on Sundays. The difference is, there was no media coverage so most people back home never heard about it.
As for looting, there was ample looting before our troops even had a chance to establish local controls.