The river was never a problem.
But the expectation was always that the levees around Lake P would overflow. Nobody expected the breaches in the areas around the canals. There is a levee around Lake Ponchatrain,,I have biked and walked on it. They did not enlarge it, make it taller, because very expensive homes would have to have been taken to make the base wider.
I don't know much about the canals except that I never worried about them.
My grandmother's house was about a block and a half from the 17th street canal on the JP side and before they got around to working on it, she would get water in the yard regularly and infrequently in the house. Another issue is what to do about barriers built to keep water that keep water in when the system is topped or breached.