Why diplomacy and defence should remain distinct institutions

Would there have been logic in merging the Ministry of Defence and Foreign Office during the Cold War?

No; related strategic purposes do not erase the institutions' distinct cultures, technical professions, and leadership requirements.

Diplomacy and military action serve related state aims, but their organizations require different skills, cultures, and management structures. The Foreign Office lacks the military non-commissioned-officer layer imagined in the merger proposal, so combining the departments would not create an interchangeable workforce. Rank equivalence does not qualify a special-forces officer to command a warship without the relevant training. Naval officers need enough technical understanding to translate specialists' diagnoses into the time and operational consequences a captain needs. A weapons-engineering officer also decides whether a repair needs a different specialist and manages the careers of the people doing that work. Those responsibilities depend on knowledge of the profession and organization being led.