Insurance does not cover "civil unrest"
Arson, theft, looting etc during a declared state of emergency are not covered by insurance.
Remember the businesses in LA during the Rodney King riots? They were SOL.
There are insurance companies that will personalize P&C coverage for you but your run of the mill insurance company offers generic coverage. Read the fine print before you sign.
NOLA has not been called a state of emergency as of yet. To do so would require the governor to give power to the feds. She still has control of the National Guard, Bush has control of the active duty military.