It can and should be rebuilt, but at a new site.
I built houses on the NC coast, as a General contractor. They have withstood the hurricanes, but the beaches have deteriorated, almost up to the pilings, on several. But, the storms haven't taken them, yet.
There are ways to do things right. ...and there are ways the gum't does them!
I don't think folks realize that once these places flood there is no going back. You can't just move in again when the waters are removed. The local politicians promising to rebuild are feeding the people are truckload of bat guano.
One thing is certain: all new construction better be built with such disasters in mind. Making a new Venice out of New Orleans might be entertaining and fun for tourism. The fact remains it is suicidal to rebuild the city feet below sea level in that 'bowl' area between three bodies of water! If tax dollars are doing to the effort, they must be spent *wisely* and not on some emotional whim. Move the city. Raise the level of the city. Something has to be done to avoid such a costly (and predictable) wipeout event from happening again.
Will this happen? I doubt it. The political will just isn't there. Instead the levies will just get taller. UNLESS, the death toll is hundreds or thousands making a strong, emotional "never again" case. Even then I have my doubts. Especially after seeing how Gov Blanco and the others did not act ahead of the landfall.