^Sure the President has to win some sort of election but is it by popular vote of the electorate or does the council elect the President from their members?
If the Federation is supposed to be a utopia, either the President would be directly elected or this council would be elected. If the council is not elected and they pick the President, then Kirk and Sisko's line about the Federation would be false, so I think the Federation would be run by a elected body. Either the President runs directly or members of a parliamentary body run for office and the President is choose amongst the elected parliamentarians.
If the Federation was run by an oligarchy, how would it be a utopia?