And would this silt deposition actually occur at a rate that would fully counteract sea level rise, just as the huge rise in sea levels at the end of the last ice age did not mean that the delta disappeared?
If so, the danger to New Orleans would be entirely avoidable by changes in local land use.
Perhaps the fundamental issue is that river deltas tend to be dynamic, with the watercourse continually changing, which isn't really compatible with a city in a fixed location. (Hence the damaging attempts at stopping this.)
On the other hand, the silt wasn't ever being deposited in large quantities in New Orleans itself, but more in other places. The delta is huge. New Orleans is famously below sea level and always has been. There's always been hurricanes. It's always been dangerous to live there and I'm not sure you can blame the dynamic nature of the river.
The river wandering is part of this. Since the silt can only be deposited where the water goes, for the delta to grow (or just maintain itself) the river has to go here and there all over it.
And yes, people die when this happens. But if you stop the river wandering, the silt isn't going to be deposited so as to maintain the delta.
Maybe it's not a good location for permanent human settlement.