It’s fairly simple. They are easy to control and they have no crises of conscience.
Imagine you’re trying to find minions who will lie, steal, kill, declare wars, commit treason, and otherwise be nasty people without remorse, and who will always do what you say. That’s a tough order to fill, given that most demographics predisposed to betrayal and rapine also tend to lack conscientiousness and other employability traits.
But pedophiles and other extreme sexual perverts can come from any societal stratum. Further, I suspect the real powers behind the velvet curtain can create sexual perverts out of ordinary people by abusing them at certain times during their physical development. This is less far-fetched than the (entirely necessary) brainwashing methods used at boot camps since the dawn of time.
Pedophiles can be controlled by both carrot and stick. Drip-feed them a supply of beautiful children, and they will love you. Remind them that you have video recordings of everything, and they will fear you.
Combine this with the soul-killing effects of sexual perversion on the amygdala, which acts as a conscience for ordinary people, and you have the best possible figurehead politician. Keep in mind that in a small inner circle of perverts, there is no longer any component of shame associated with pedophilia et al. Actually, we can observe that societies of perverts tend to applaud individual particularities (an extreme manifestation of progressive “tolerance”).