I normally don't shoot if I think a shot is over 300 yards. For game, as opposed to varmints, it's about how close you stalk, not how far you shoot! Last Thursday I did cleanly kill a whitetail buck at 322 yards, one shot, but that was a very rare exception because I knew the range and my rifle exactly and had a very solid rest.
I have all my big game kills recorded in a journal and could calculate, but I estimate that for over 80 big game kills to date, my average range was less than 100 yards. And I DO hunt the wide open prairie as well as forest habitats.
I think that I'm a better than average shot, but don't know how that could be measured. I practise a lot on my private range, shoot a couple of boxes of shells most every week except in winter. I can easily keep all my shots on a 14" steel gong at 250 yards any time, but only with crossed stick rests, bipod, prone, or some other very solid rest. Any significant wind, or shooting from less steady field positions makes shots over 300 yards unethical because of the high chance of wounding - at least for me. But then I believe that a shooter should be prepared to punch his tag after drawing blood, whether or not the wounded animal is recovered. That cuts down drastically on "hope shots" taken at extreme range or at briefly glimpsed running game. I hold guests invited to hunt on our land to that standard. So, I think that hunters should shoot at any opportunity when they feel confident they can make a good shot - whether that's 50 yards or 500. Standing shot or running. Just live with the consequences.