Most people have morals and wouldn't have sex with an underage person, nor murder someone, just because their boss told them to. They would tell their boss to go fuck himself.
People have been blackmailed for scandalous actions long before video to record the incidents. No technology is required.
Visiting sketchy sex-related businesses or doing drugs is pretty par for the course in both Eastern and Western business culture as a form of trust-building between parties.
I can definitely see the level of "sketchiness" increasing as you climb the power ladder.
>the famous article from Sultan Mehmed II the Conqueror's Law of Governance states that "Any of my sons ascend the throne, it's acceptable for him to kill his brothers for the common benefit of the people (nizam-i alem). The majority of the ulama (muslim scholars) have approved this; let action be taken accordingly."
https://www.dailysabah.com/feature/2015/08/07/the-history-of...
As every such cabal would be much more effective than a lone politician, eventually power would entirely shift to competing cabals bound by child sex blackmail - making it impossible to dismantle externally, because both the executive, the judicial system and the biggest media would be controlled by people in such arrangements. Media in particular would have the main job - in case of any genuine leaks, mix the truth with outlandish claims to discredit it as a dumb conspiracy theory.
The game theory works out so nice I don't see any alternative, it's the stable state of the political system. I can see it being murder though, if disposing a body is much easier than my estimate.
In non-Western societies it could be something else. In North Korea, being filmed shitting on a photo of the current leader would work much better I guess.