I love the spirit of this suggestion. I've been thinking all day about how an important part of the mores and norms of Stack Exchange is that we have collectively agreed to be nice. I've noticed this most when somebody shows up and unilaterally decides that they have a right to be non-nice and then gets offended when someone in the community calls them on it...
Anyway, yes, we care about being nice; that's a fundamental part of the joy of participating in Stack Exchange, it makes the world a better place, it makes the Internet better, and it leads to the extremely high signal-to-noise ratio throughout Stack Exchange.
As for whether or not we can rank based on it... that's leads to a more interesting sociological question.
Would a politeness score really influence behavior? It might, to some degree. I would estimate that about 20% of Stack Exchange users are actually incentivized by our reputation and badge systems, while the other 80% are slightly amused or indifferent. That's OK, because the reputation system and the badge system still serve for everyone to understand what we value as a community. Even if you don't care about earning reputation, you understand, for example, that this community values answers that receive a large number of upvotes.
That said, there is some complexity involved in adding a "politeness" feature. It's one more thing new users have to learn about, so it might serve as a barrier to entry. We'd have to find some place to put it in the user interface where it wouldn't add to the clutter. And there would be more work involved in "evaluating" an answer. Instead of just saying, "Yes, this answer makes me happy, thumbs up!" you have to decide (a) whether it's factually accurate and (b) whether it's polite. So the mental burden of voting just went up a bit.