I guess mechanical complexity's advantage, in a game perspective, may then be that it makes the decision-making mimic reality more? This can have ingame effects in turn, especially in tabletop gaming. For example, imagine a game of draughts, same rules as usual, except that you can pick from any of ten colours, which make literally no difference to the game. A mechanic has been added that is, in technical terms, useless. What it does, however, is allow the players expression in how they play: suddenly, you could have team colours, or players adopting (or having grudges against) certain sides for absolutely no rational reason at all. In other words, more complex mechanics may reduce skill input, but they might also increase the storytelling potential of the game.
As another example, think D&D. Goblins, gnolls, and kobolds aren't really actually honestly very different in mechanical terms, they could just be a "generic evil humanoid" entry in the monster manual for most purposes. The decision "hunt down the goblins" vs "hunt down the kobolds" which an adventuring party may be faced with is pretty limited in its strategic impact. On the other hand, it might have a lot more knock-on effect regarding the players and the story they're telling.