It's not clear that the Federation president is elected. Has there ever been any discussion of federation politics ever? Even on an aircraft carrier someone would mention an election.
Trying to infer post-scarcity economics from an internally inconsistent bunch of TV shows and movies where it's pretty clear there was never much thought given to the matter seems like a waste of time. I lost interest in the article when it tried to do this, Iain Banks's Culture which is much more clear about its economics still doesn't answer basic issues such as "why can't anyone have x?" Or "what if two people want the same x?"