Actually the Egyptians did, bigger and grander, a few millenia before.
Alexandria
Actually this is a fascinating subject, but perhaps more appropriate on a separate thread.
There are several dynamics at work. Yes, silt is getting carried out to sea, but also deposited in and around NO the whole time. The "filled-in" area is a long ways further into the gulf than it was 500 years ago. How the "new" land later settles and becomes lower than the river is a whole other dynamic.
Controversial NOAA report says Louisiana's shores plunging fast — are Texas' next?
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Instead of minimal geologic subsidence along most of the Louisiana coast, as previously thought, the state's entire coastal region is sinking at least 5 feet every century.
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"You're draining almost the entire North American continent into the Gulf," Berman said. "The cumulative weight of that is immense."
So immense, in fact, that the Gulf of Mexico is pushing down on the Earth's crust, making an indent. For coastal regions along the Gulf, it's like being at the edge of a trampoline with a bowling ball weighing down the center: The natural inclination is to slide toward the center. The toothpastelike shale layer facilitates the slide, Berman said. Geologists call it gravity gliding.