But I guess we as human beings still have minds from 50,000 years ago and we want to see a leader to our tribe. The concept of shared leadership is brilliant, but too advanced for our stone-age brains.
I think the evolutionary psychology line is going too far. I don't think anyone is suggesting that losing the president will make us all leaderless and lost. Instead, that losing the president is a substantial blow that's best avoided. The reason for this is that the "shared leaders" you describe do not have equal seniority. So if you lose the top one, you still require a reshuffle and there will still be disruption. Further, the president is the figurehead of the nation and it is a blow to morale if he is taken out. For similar reasons, there was a big security boost around the statue of liberty following 9/11. Symbols matter, that's all.