And there's a flip side. People have incentives not to kill as well.

Think you might be focusing on PK and missing some RP opportunity here.

I might be missing something but I can't see a down side to this.

Just make people who are stunned buy another person not count to axe count or phylacs.

What's more give edgepoints as a regular kill for people who don't kill but leave an unconcious character. After all they would (presumably) not get any gear unless a thief or possibly an orc.