I think its lack of a correct enough specific term. I may kill a rat or a bug because its a nuisance, someone might kill some species for fun. Killing a deer with the objective of eating it is fundamentally different than killing it just to kill it.
Given that many non-hunters think we "just like killing" people searching for a distinct word makes sense. Harvest while maybe not quite correct may convey the meaning they are going for, anyone knows that harvesting an animal involves killing, we dont invite them back for tea and receive back straps as a gift. But it emphasizes the food aspect over the killing aspect.
I do get your point but I think its that we lack the right specific word and the imperfect meaning of harvest has some advantages over the imperfect meaning of kill. Around here in 95% of conversations neither word is used and "did you GET a deer" "how many grouse did you GET" is a far more common term.
Either way its not something Im loosing any sleep over.