I have a similar hypothesis (which I don't believe, but still). Suppose there are no psychopaths. As is well known, people's choices of leaders are heavily influenced by biological biases such as height, social dominance and other "alpha male" traits. If there is no need to suspect malice, communities could suffer a runaway effect of increasingly biological selection of leadership, the same way it seems to happen in most herd/pack animals (where a smaller male basically can never become a leader, even though the correlation of size and intelligence is less than 1). But psychopaths can "supersignal" beyond even the most impressive neurotypicals. With some bad apples, we feel the need to check if signals correspond at all to the substance, and correct for personal behavior and long-term ability to deliver on promises.

I understand that you’re just using analogies, but since psychopathy appears to biologically instantiated and heritable, I’m not sure they’re very useful.

More concretely, it’s a neurological variation that is “fit enough” to survive within human populations at a low threshold, so it persists. There’s no “guiding hand” beneath it all.