An OP is motivated to keep their comment thread awesome: having better comments leads to more upvotes on the story. And, on a personal level, the OP would be less likely to upvote snark against their own story.
The obvious downside would be that the OP could effectively censor opposing ideas. However, I don't think this would happen that often: counterpoint comments generally do pretty well on their own, and would probably still rise to the top even without the OP's help. (Of course, the best OP's would recognize the benefit of discourse and promote these comments anyways... but not everyone is perfect)