I think you're right that the relationship is complex and you probably wouldn't want to optimise just around empathy/altruism. In particular highly empathetic people can sometimes run into problems with cognitive bias around large abstract concepts or numbers. I'm guessing there might be a "sweet spot" for leaders of having enough empathy to want to do the right thing, but not to be overwhelmed by emotion and unable to make difficult decisions.

I'm very interested in possiblities for that sort of test, but it could be tough finding something that can't be gamed. Perhaps some research looking at a range of candidates for (perhaps multivariant) correlations with morally good and effective leadership decisions needs to be done. Actually... surely someone would have done that... though I haven't run into it so far...