Why bother re-building New Orleans?
Because New Orleans is located where it is because a commercial need has existed for a port on the mouth of the Mississippi since it was founded in 1712 until the present. The location of the city has everything to do economics and trade, and absolutely nothing to do with arbitrarily living in a marsh.
From the standpoint of national interest, national needs, there must be an infrastructure in the New Orleans vicinity to support the commerce of the mouth of the Mississippi River. The Port of South Louisiana depends on NO being there as the "hub" of its operations. This is not optional.
Oil, coal, grains--import and export. What occurs in that area cannot be done anywhere else. It's not like New York City, whose financial paperwork can be done in Omaha via electronic communications. The lower Mississippi is physical, grubby-hands work.
However, 500,000 ppl don't need to live there to support a port.
So: It's foolish to build a city in a below-sea-level bowl. No magic to it, just jack it up. That was done in Galveston after the 1900 hurricane. Get the non-historic area above sea level via dredging into leveed compartments and then do the flood-protection levee work. Design and construct the new levees for Category Five.
Next thing, looking ahead: Clear those damn trees back from highway rights of way. Scenic is nice, but things go all to hell when the roads are closed from storm damage and downed trees and power poles.
Then establish building codes that require homes be able to ride out a class 5 hurricane and the storm surge that's appropriate for the building site location. For New Orleans, since there are no guarantees about the levees failing again, no residences would be allowed below high tide. Any construction below sea level would be reinforced concrete.
Do this right and New Orleans could be a very nice place. Either that, or make it a city of houseboats and floating piers.
But will that be done? No. Everyone is going to be a sentimental moron about it and restore everything to the status quo, make a half-assed attempt at improving the levees, screw that up, and the next big storm NO will get destroyed again.