If New Orleans was struck by another hurricane as big as Katrina, should they rebuild?

Yes, they shouldeven if that were to happen.

New Orleans has to be where it is, and yes - rebuilding was not and will not be optional. If nothing else, New Orleans' port is the largest in the western hemisphere in terms of tons of cargo handled.  That can't be moved.  

The reason New Orleans flooded was because the US Army Corps of Engineers negligently built part of the flood protection system, and the part they built was what failed. The reason the USACE negligently built part of the flood protection system was because the Clinton administration secretly took funding from USACE projects all over the USA to cover the budget for the "Big Dig", a commuter tunnel under Boston's harbor. In the case of New Orleans, 30% of the budget for the flood protection system was secretly diverted, and the result was a Potemkin flood wall.  That means the rebuilt flood walls > looked < correct on the surface, but the below ground supports only went down 11 feet instead of the at-least 35 feet required by the specifications. It was exactly those parts of the flood protection system which failed during Katrina, causing 80% of New Orleans to go under water.      

a hurricane is nothing but a storm .. when its over you clean up and patch up what you have to .. do-nothings sitting around waiting for someboduy else to do it yeah .. let um rot ..