technically, it wasn't built below sea level, it sank after it was built. but the act of building and developing it is at least part, if no the primary, reason it's sinking.
saving the part that's above sea level and moving on from the rest seems sensible, but much or most of the quintessential new orleans is the part that's at/below sea level. might as well find somewhere new and start over at that point.
large cities with significant cultural influences have been abandoned before, just not in our country/culture (that i'm aware).