I was a grad student at Tulane in the late 1980s and took many field trips out to the Gulf swamps. Some of them were to help a researcher studying sedimentation rates. Biologists knew then that what is happening now was going to happen. Even then, it would have been expensive to do anything about it, but about one hundredth or one thousandth what it costs now. And one millionth of what it will cost in a few years.
There are two main causes of the problem. Levees along the Mississippi push all the sediment out at one spot near Venice ( and make Gulf dead zones) instead of winding up at different spots all over southern Louisiana as the river makes itself new channels every year.
The second issue is the oil and gas industry which cut channels all through the wetlands to move equipment and build pipes. Salt water intrudes along those channels and kills the vegetation. The dead vegetation doesn’t hold onto the “jello” soil anymore, and the whole thing washes out to sea on the tides. There are early satellite photos of the area, which look like green wetland, and recent ones where the whole thing looks like lacy spider webbing on water.
And, yes, diversion of the river in its current state of pollution and fertilizer load could well create more problems than it solves. Telling the oil and gas industry to restore all the wetlands they ruined is probably also “too expensive.”
By the way, the only part of New Orleans above sea level is the very old part of town and the sliver along the river. Not a lot of sanctuary, especially when sea level rises. There is no land bridge to the mainland. And the causeways would have to be raised.