There is an additional problem; leaders are not necessarily trying to lead all the time (or so I think).

My personal experience is for example that I had rather leadership episodes in my life than a continuous quest for alpha male position. At times I didn't see a need for leadership, other times I preferred to opt-out of group dynamics or oppose existing leadership. And then there were episodes when the system cheated me so badly that I preferred to oppose it by making a fool of it; identifying and exploiting its holes. To lead a pack in a futile effort to oppose the system seemed pointless, and I didn't try it.

You might end up with false negatives even in great natural leader test regimes.