There are many engineering solutions for storing large amounts of excess rain, some cheaper than others. Los Angeles built the huge Santa Fe Dam which is a normally dry flood control dam, but later they dug large spreading grounds next to it where almost all excess water is now sent underground. The cheapest solution of all might be to breed beavers to build mini-dams all over, and encourage them by diverting the creeks around.
It appeared to me that the flood control guys knew what they were doing and were prepared to act.
Early on. as the water rose, they unfurled what seemed to be stiff red white and blue sheathing on the river side of the levee. As the river rose, the sheathing formed a barrier to protect the levee. As it rose to a certain level above the midline of the sheathing they brought in the big back hoes to breech the levee and allow flooding of the areas beyond. There were several videos of such breeches. The breeches prevented over topping and protected most of the levee from destruction.
The problem was that the rate of rainfall was greater than the levees could accommodate. They had 6 or 7 inches of rain in one day on more than one day. Some areas upstream of the three gorges are being described as historic marsh land. The levees protected this former lake/marsh land that was apparently drained for crops. It was a huge area. It is being described as the natural flood area that historically protected the populated areas down stream.