That will be an air traffic nightmare simply because it rotates with the wind.
Approach procedures (from enroute to landing phase) are complicated enough as they are. As they currently stand, there are several approach procedures for any given major airport, with each approach chart being tailored for a specific runway alignment. Having a runway that rotates 360 degrees in the wind would require 360 different approach charts.
Without a lot of highly advanced and fully automated flight systems, an airport like that would be a major hub for midair collisions or near misses. No human pilot would be able to handle that kind of workload while hand-flying the airplane.