I am suggesting that there is a natural inclination towards a particular set of people for certain types of positions (as the data shows), and to select for variables against this inclination for sake of diversity seems artificial.
In my experience of management, cohesive operation likely isn't a viable position for efficiency, unless the team is incredibly specialized. Fast paced environments coupled with non-specialized personnel is almost begging to be coordinated, and I've seen very unpopular but smart decisions made by sufficiently authorized personnel. Who, of the two dichotomies, would be more efficient at seeing this through? I would almost exclusively select EXTJ's for such a position, though I do acknowledge they are not the only type able to efficiently carry out business operations.
Now specialized teams are something else altogether, and something I personally strive for in a work environment. If all ten cogs in a machine know exactly where and why their gears mesh, is such a controller necessary? Perhaps, but because of the unilateral operation I don't think either dichotomy would be more or less efficient at the position. This is likely where sensor/intuitive bias would come into play, more so than thinking/feeling.