The question is, if you are going through the effort to catch them. Which includes owning and feeding extra dogs (catch dogs). Handling more dogs on a hunt. Puting dogs at a higher risk for injury, and making more work for your self. Why would you not keep them alive if you allready have them caught? If you just want to kill them why not bay and shoot. Its less work and less danger of dogs getting cut down.
Waylon
I can answer this question for myself.
A few reasons. I enjoy the sport of it for starters. I have to catch hogs in half the places I hunt. Maybe most of them. I'm not allowed to used firearms on these places so I have to feed a catch dog.
I also hunt for land owners that just want to get the hogs gone. We bay and shoot every dang hog we come across on a hunt and kill any pig we happen to catch. It sure makes for a lot of skinning and cleaning but that's part of it. For eradication, I don't think there is a more affective and productive way to clean out the hogs in an area.
I'm old school enough that I don't like seeing meat go to waist if I can help it. I don't eat boar meat either. I just don't care for the stinch but you can change those same hogs out and in a few months they will make some real nice sausage for me or whoever I give/sell it to.
That's my reasoning but I am a practical thinker like you and I don't like the idea of feeding a catch dog or having it on my place but that's just me.