An AA gun of this size would have been poorly suited for tracking aerial targets.
True, but smaller caliber rounds do not go as far up or carry as much stopping power when they get there..
Yes perhaps low flying fighter-dive bombers but bombers flying at 6000+ meters won't get reached by "aa-machineguns". And the higher the plane flies the slower it will apper to be moving making tracking easier
Smaller caliber AA is used for close in defense of planes doing ground attack (like strafing as compared to dropping bombs). Larger caliber AA is used to lob Flak shells so that planes fly through the flak, no direct hits are needed. Flak is generally used for higher altitude targets. In fact, you would want the shells to explode ahead of and slightly above the planes you want to shoot down. All it takes is one piece of shrapnel the size of a marble to get svcked into a jet engine and the plane could go down.
Flak, while effective at downing airplanes, was more used to upset the bombing runs as planes need to be on a set path at a set speed for a period of time for the bomb sites to do their job. Putting a bunch of flak up in the path can make the airplanes jink and move around, making accurate bombing problematic.
Almost all large caliber guns, 88mm or above can be used for Flak or more normal Ballistic firing. It is all in how you point the gun and what shells you load.