Jeff, it has been on 'the edge' for most of 100-150 years. The Old Quarter is actual built on the HIGHEST GROUND ... less flooding. Plus there are many brick building but the WOOD building burn FAST and HOT.
Having live near Philadelphia for years ... Ben Franklin (and his public fire department) required joined housing (rowhomes) be built with all brick or stone exterior.
The 1700's rowhouses are not perfect .. seems the wood floor joists do ROT and the row house falls into the basement (bad roof, abandon home, prior interior fire). Plus the taxes in Colonial Philadelphia was based on the width of the house ... narrow lot row homes on 3 floor plus a basement.
And most of the Old Quarter in NOLA is brick housing .. for the same reason. And had outdoor kitchens not attached during the living part of those homes.
There's another reason N.O. is on the edge of destruction. Well, maybe not destruction but economic irrelevance. The Atchafalaya River takes about 1/3 of the flow of the Mississippi at a location very close to that spur in the extreme western part of the state of Mississippi. It is easily seen on Google Maps.
Left to itself, the Mississippi River would abandon its current course and take the shorter, steeper path down the Atchafalaya basin to the Gulf of Mexico through Morgan City, LA. Sooner or later, it will happen. It almost happened in 1973. The US Army Corps of Engineers has been fighting the battle to keep the Mississippi in its current course. Someday, it will lose.
When it happens, what is now the Mississippi River at New Orleans will become a salt marsh -- the Port of New Orleans will cease to exist. The economic impact on the many chemical plants and petroleum refineries along the Mississippi between Baton Rouge and N.O. and the entire US economy will be devastating.
Do a Google search for "old river control" if you are interested.