Shortround6
Major General
You may be close, estimating costs based on weight in action a bit questionable but it is all that we have.
As to the worth, the Germans tried 2-3 times and the first try, the 5cm Flak 41 showed that while such a gun was desirable, the 5cm Flak 41 was not it.
5 cm Flak 41 - Wikipedia
Ian V. Hogg's book on German Artillery says.
"It was unstable when fired, the center of gravity was so high it was also unstable when being towed, it was difficult to conceal, it could not track targets fast enough, the sight was too complicated and was a poor calculator in the Bargain."
Hogg's book has some different numbers than Wiki in that it shows emplaced weight and practical rate of fire (130rpm) and a much more optimistic effective range.
The 5.5cm Flak Ger 58 was a gold plated, cost is no object, goal was 100% destruction using a 6 gun battery defending high value targets. This never made it into service.
This started when the Germans discovered the 5cm shell size was unsuited to the job needed. It was impossible to design/build a shell that held the desired amount of explosive that would remain stable at the high velocities demanded. Back to the drawing board and the move to the 5.5cm shell size.
The only other examples are the post war Bofors 57mm guns and the Soviet post war 57mm guns.
US and British pretty much jumped right to 75-76mm guns using proximity fuses.
The British did have a long and torturous path with the 6pdr 6cwt AA gun (which only shares bore size with the host of other British 6pdr guns) and would up with a twin gun that weighed over 24,000lbs in action and managed 35 rpm per barrel when everything worked right, which it much more often than not didn't.
This Path took from the Idea in 1940 to the specification in Jan 1941 finally, after many twists and turns to the cancelation on March 30th 1945.
Work on a single barrel continued for a while after the war that lead to good information on high speed loading systems but not much else.
