I meant that it was not the kind of range where people expected to shoot effectively, though I'm sure there were number of kills even past such extreme ranges. The convergence of the guns was usually set between 200-300m. Some aces preferred even closer (and indeed, it's in Dicta Boelcke to only fire at close range).
Which brings up another issue which hasn't been mentioned in this thead yet, and that is gun placement. If you have guns in the wings, then convergence matters quite a lot, and evasive maneuvers by you or the enemy can get your bullets very far off their intended target. However guns mounted in the nose of the plane don't have these sorts of issues.
BUT
there isn't much space in the nose of a plane, so you had better make that gun count - the Germans routinely tried to get a 20, 25 or 30 mm gun in that spot. The Americans had a few attempts too, notably the early war P39 air-cobra with a 37 mm nose gun that had the engine built around it. However for the most part the American 'solution' was to line up a bunch of guns in each wing. These guns were necessarily limited in size by the width of the wing, and the .50 cal machine gun was the best compromise out there. In theory you could put 20 mm guns in the roots of the wings, 0.50 cal's further out, and 0.30 cals' on the edges, but that's a horrible mess for trying to set up all the different gun and bullet firing characteristics, ranges, ammunition capacities, and firing switches. Using all one caliber eliminated all those issues. The Germans and to a lesser extent the Russians stuck with a few high powered guns at center (or wing root) and 0.30 cal's other places as a backup.