I agree, complexity doesn't equal good design by default. Complexity for its own sake makes the game 'spreadsheety' as Howard put it. That doesn't mean that complexity and different layers of immersion are inherently bad on the other hand (I know you didn't say that, but sometimes you have to fill space with important messages).
My idea of good game design is a game that stands as itself. The approach of having every player 'do what they want to do' (in terms of outside factors) creates unneccessary complexity imo. You have to mind every kind of player out there in such a scenario, which leads to many optional ways of accessing the game as a game. In an extreme case, this could lead to many different games inside one. It's much easier to not bother with that, especially since most players play to have fun and a good time. They won't care if the game has but one difficulty level for example (bold statement, I know, but most players I know would agree). Choices should come inside the game, not outside.