This would have to be done ahead of the hurricane, and then all the equipment moved out of the area before the storm hits. To me this would seem to be the biggest drawback since it requires an accurate forecast and lead time with dangerous and or expensive consequences. That means it's subject to forecast error, e.g. they could pump out near New Orleans and watch the storm pass by to Texas.

Beyond that, if I remember correctly, Katrina intensified over the loop current and deteriorated near the coast. It's common with N. Gulf coast storms due to some combination of landmass dryness, latitude, and other local factors. Regardless, the Storm Surge, the part of the hurricane that devastated New Orleans and much of the Gulf coast did not seem to respond significantly to the wind and structure reduction just before landfall. I don't see any expectation that this plan would reduce surge, and I don't see any reason to believe the damage from Katrina would have been significantly less with reduced wind..

Charley would have been a better example as it's intensification was very close to land and made landfall and had heavy wind damage but little surge damage. Knocking 5-10 mph off of the top winds there would probably have saved some money.

Regardless, this seems like a futile waste of time to me, the money would be better spent helping victims and designing better future storm defenses (wetland protection, stronger structures, better evactuation plans, etc)