Why a German 5-inch dual-purpose battery was unlikely

Would Scharnhorst and Bismarck receive a German 5-inch dual-purpose gun if it were available before World War II?

They should replace much of the separate secondary and anti-aircraft battery with it, but German committee decisions make that outcome unlikely.

A successful 5-inch dual-purpose weapon could combine work otherwise divided between separate secondary and anti-aircraft guns. An estimate could begin by adding the historical mount totals from those two batteries. A slightly smaller number may work if fewer mounts receive better individual firing arcs. The technical simplification is plausible, but the Kriegsmarine's committee structure was unlikely to approve and implement it in time for Scharnhorst or Bismarck.