An average is a better indicator to the user of how well they are engaging with the site. It only goes up if the user consistently posts worthwhile comments, which rewards being selective about when you post and thoughtful about what you post. Fewer and better is encouraged. Consistently good is encouraged. Lousy comments (like one-on-one arguments and "Me too!") are discouraged even if nobody votes them down.
This bridges the gap between two existing forms of feedback: total karma (which nobody really cares about, even though it's on every page) and the voting on individual comments (which is the closest thing we have to an indicator of comment quality), and gives the user continuous feedback on how much value they are adding to the site. It makes it much easier to know if your commenting is getting better or getting worse. That is, it is much easier to tell that my average is up or down from the last time I looked than it is to detect the fluctuation in the rate at which my karma accumulates.
Even if lousy comments get voted up--as happens when, for instance, someone first-posts an opinionated quip on a controversial submission and people swarm to vote in agreement--the impact on the user's average karma (which better reflects their value to the community) is much lower than the immediate spike in their total karma (the feedback they currently see). You don't have to stop people from writing such comments--just give them a smaller cookie when they do.
Obviously you can't make anybody alter their behavior over a number, but I think most here would if given a number that they could trust as representative of the shared goal of keeping this place from sucking.
tl;dr average karma is better feedback than total karma