Ken,
I hunted almost exclusively with a pistol of some sort for 3 years. Why? For the extra challenge and secondly a pistol is a lot lighter/handier than a rifle. I live/hunt in Pa and in the pre-QDM days the odds of seeing, let alone shooting a big buck were quite rare. So to make the game much mo' interesting, we started hunting with pistols. Hunted with hand made recurves the previous 10 years with alot of success on 6-8 point bucks - none of which would impress anyone.
Killed most of my deer with an 06 Encore pistol, a few with a 308 Bellm and 30-30 in the Contender, a few with my Ruger Blackhawk 44 mag, and 1-2 with my Smith 357. Hunting with a pistol is great fun - especially if you ain't overly concerned with horn size.
I even had a 350 Rem mag barrel built for my Encore to take Elk hunting. Still haven't toted it for Elk but did kill a doe with it 4-5 years ago.
Between Dad and I, we have an arsenal of interesting pistols that we hunt with. We usually designate a doe day and establish rules accordingly. Mostly its no rifles allowed - any pistol will do but we've had some interesting rules, most of which anyone can assign to another. I assigned my dad his 45-70 Trapdoor with bayonet affixed, SS german stalking rifle, a 8.65789 x 46 or some such designation, 7.65 Argentine Mauser, 416 Rigby for particular hunts. I get lucky because I don't have the extensive arsenal he has, although hunting with a flintlock has proven interesting at times for me.
Anyway, the main reason is added sport with alot of fun thrown in for good measure.