Speaking of my own experience and a couple other lion hunts I've tagged along, with a bow the houndsman has more concern for the dogs. Often the arrow stays in the car when it bails and runs off. It's a hazard for the dogs (sharp pointy thing that can harm the dogs). Catching the cat and getting in a few bites is a reward for dogs, as explained to me. Doing that with an arrow sticking out is not good.
The houndsman I was with (a friend and fellow guide) wanted to lease the dogs so they didn't immediately chase the cat when it jumped at the shot. We treed my cat twice. He bailed the first time because we were leashing. We leased at the second tree also. We watched pretty closely to see where the arrow ended up. He walked his dogs up to the cat in leash, and we verified if the broad head was sticking out, had fallen out, etc. Before he even let the dogs get close to the carcass.