It doesn't seem to me that players who like more than one way of playing aren't capable of deciding "I feel like a cultural victory/one-city challenge/spaceship win/early world conquest today" for themselves; nor does it seem to me that if you have players who only ever want to play for, say, conquest (the poor dear misguided souls) that the game should be forcing them to play in ways they don't like, or alternatively, artificially handicapping their ability to play the way they do like. I don't see how either of these lead to better replayability, and the suggestion that players will tend to the same thing by force of habit regardless of what they actually want or consider fun is a bit insulting, really.
I'm thinking that I should rephrase my argument from 'uniques allow for more strategic options' to 'uniques allow for a wider array of possible strategies for the player to choose from'. They most certainly do that, and whilst I see your argument that in a given game they may limit your strategy (although not compulsorily), they do offer a far greater array of possible strategic paths which you can possibly explore.