Game Culture: Do More Game Mechanics Equal More Fun?

Reading through internet forums, I see an idea recur constantly: more game mechanics do not equal more fun. This idea feels incredibly frustrating to me; the argument essentially says that a game should focus on only a few mechanics and refine them. Though I have found plenty of arguments against adding more mechanics to a game, I have struggled to find anyone arguing against this. I want to provide a more in-depth discussion, highlighting the different philosophies and giving my opinion on the discussion.