My daughter got her PhD at Tulane so we made more than a couple trips down there. I believe part if not most of the problem in New Orleans is that part of the French Quarter may have fallen as much as 16 feet over the last 200 years or so. We did the swamp tour and the guide pointed out that we were at essentially sea level there but still 16 feet above Canal Street.
No doubt some of what you say is true and a factor about the French Quarter. However, the levies were not just breached, they failed in many cases. And that speaks to the incompetence and corruption in many gov contracts, especially in one of the most proudly corrupt states in the country.
A native of New Orleans once mentioned that much of the city was built on altered land filled with compacted cotton bails. In any event much of Louisiana is subsiding former marshland without silt deposits to compensate for compaction.