I had a discussion with DOW a few years ago about this. As most handguns do not meet the requirements for big game, carrying them would be suspicious for hunting with an illegal weapon/method. By having a small game license, most handguns become legal for small game use.

Regarding BLM land, it is federal property and concealed carry is allowed if CC is allowed in the state however there was something in the regs (I will try to find it again) about not being able to small game hunt during big game seasons or something like that.... I'll see what I can find on that. I have both CCW and small game permits (and I don't hunt BLM) so it's never been more of an issue for me.