Actually, the hunting band should probably be referred to as the hunter/warrior band.  The two functions appear to go naturally together.  If you’re proficient at using, say, a spear or a club or an arrow against prey, you’re not going to lose that proficiency when the time comes to use it against a human opponent. 

Moreover, hunting societies seem to be, by their nature, heavily prone to territorial squabbling.  Nobody has clear boundaries, and when you're pursuing game, it's all too easy to get closer to the territory occupied by "the other people over there" than they'd like to have you.  They feel they need to push you back, you feel you're just pursuing your legitimate interests, and you clash.  For this and an assortment of other reasons, hunting-based societies tend to be almost continually involved in some sort of fighting.

Now, a society that lives in a state of more or less permanent warfare is going to produce its share of miseries.   This principle is fairly well recognized, and has even become central to a kind of contemporary "testosterone as pathology" point of view.  But there are also certain benefits in the social order that such a society can foster.

When the mainstay of your local society is a band of say, 20 to 40 guys, and your survival depends on being a credible fighting force, your social order is going to have to be free of certain rigidities found in other kinds of societies.  Among other things, the leader can’t require his subjects to adopt a manner of constantly fawning, timid deferentiality.  That just doesn’t go with being a warrior.  So in a hunter-warrior society, everybody gets to "stand on his hind legs," claiming his position and status more on the basis of actual, demonstrated prowess.  That’s a good thing.

Pretty much the same principle that confers status on a powerful warrior applies to somebody who’s very smart.   You don’t have the luxury of ignoring him, if you want to survive;  and in the act of listening to him and heeding his advice, you likewise accord him a measure of social standing.

Also, since who’s strongest or smartest is going to vary from generation to generation, you can’t have rigid hereditary social titles or classes or castes.  The precariousness of your survival obligates you to continuously bring the most capable people to the fore. This is essentially a variant of the principle that Jefferson called "natural aristocracy"—of social position based on ability and accomplishment, rather than inherited titles.  Far from being a bad idea, it lies at the core of some of our most commendable American beliefs and ideals.