RE: Do we "owe" it to anything/anyone to be accurate shots ?
IMO if you can make a clean quick kill with your long bow then use it. Just stay within your limitations for distance like most have said. If you can hit "the pie plate" at 20 yards with the long bow and 40 with a compound and you take the long bow for hunting that day just go to a stand that will offer shots 20 yards or less.