I agree that intellectuals often lack street smarts and aren't likely to make for effective managers. But I was thinking of long-term productivity, as understood from a big-picture perspective. Intellectuals are supposed to specialize in big-picture thinking. Their head is in the clouds, which is why they don't know how toilets work.
The question is whether our day-to-day productivity is self-destructive in the long run, whether our entire self-serving, consumerist societies will prove ultimately to be counterproductive, whether we're racing towards our downfall. Are plumbers supposed to specialize in that kind of subversive perspective?