Voyager did this already with the Hirosians (spelling and phonetics questionable - it's been a while).
I never got the impression that those shows were anti-hunting. I would compare them to the movie predator which I don't think was anti-hunting. From what I heard about the upcoming show, Archer declares that Earth stopped hunting generations ago. Which is interesting since in the opening show a farmer shoots a klingon with what looks like a (laser) shotgun. Why a farmer would have a hi-tech gun if there's no hunting, and Earth is a peaceful paradise, is never addressed.
I don't remember getting an anti-hunting message from that episode at all since the scene you describe is only used to give a reason to launch Enterprise.