To be fair, I think this is quite different. Many of the NOLA PD likely lost their families, etc. in the aftermath. There was bound to be attrition. Those left were stuck w/o communication, thereby losing command and control. The thugs took advantage.
Now in a loss of cilil order, the PD is outgunned - in that position, better to not engage the enemy. THug activity would prevent the FD from working, and without efective security, they are smart to not go out and killed by thugs.
Meanwhile, the mayor and governor pretend it isn't going on (or the loss in civil order isn't all that bad), and delay asking for reinforcements. Their orders shifted from "don't worry about the looting, focus on resuce" to "skip the rescue, stop the thugs." How's that for command and control?