Another reason this was done was so there was no blood trail left on the ground. Wolves, and enemy dogs could follow the bloodtrail and scent from it even at night. By barking the squirrel, the animal was killed off a high limb, where it would be unlikely for anyone on the ground to see where the shot hit the limb. Then all the hunter needed to do was conceal his own tracks, and get out of there.
The brains taste sweet, and in a country that was short on sugar, anything sweet was a welcome change to a meal. We take so much for granted these days with our supermarkets and cheap food, that its sometimes hard to really understand what it was like for people who lived in this country in the early years, when roads, and stores were miles away, and sometimes more than a da';s travel by horseback to reach. ANy hunter who came across a beehive,or honeytree, no matter what he was hunting, would stop and retrieve the honey, which was more valuable and more rare than a squirrel, deer, or anything else he might hunt.