Exactly, an elected position would come with even more publicity, actual responsibilities and the possibility of being held accountable for his actions.
It's far more convenient and efficient for him to stay out of that system and just play it from the outside.
Owning a bunch of hotels is a fundamentally different type of power than owning a demographic database + messaging system used to manipulate people's moods.
Having full control of the platform a large portion of the population depends on for news and communication could help him evade much of that.
The only reason he would want to go for public office, at least I could think of, is to influence government policies. But he already has an army of experienced and well-paid people doing exactly that.