About the 2 faction problem, theoretically 50% of each faction will be gone. Chances are big that the power balance remains the same. But you can idd argue that making 1 faction completely dissappear is also 50% and statistically possible.
About the influential people (let add geniuses to be complete). Those persons are not unique, nobody is irreplaceable. Someone else will step up to be equally influential, Someone else will figure stuff out.
The reason he choose that action is not to be biased and give everyone an equally 50% chance of survival. In his eyes, a cleaning lady deserves an equal chance to a CEO.
First point: fair enough, I see the flaw. But then we’re changing to a more ethical dilemma: does a charismatic person deserve more chance to live?
Second point: with half the population left, there is more time to solve things (caused by humanity). Global warming, for example, will likely be solved by just the snap alone.
Maybe he could have made it that every female can only bare 2 children, that would gradually reduce population. But that would put a huge strain on the younger generation to take care of the elder.