I think they're overlooking the effect on the atmosphere. If the water will all flow to the poles, so will the air. If the difference in distance to the center

I think they're overlooking the effect on the atmosphere. If the water will all flow to the poles, so will the air. If the difference in distance to the center of the earth is 21km then there would be little air left at the equator -- it would be like standing on Everest, or thereabout. Plant and animal life would not survive across broad regions of what is currently inhabitable land. Further, the water at the poles would be extemely deep, and subject to cold (winter) temps year.