what the response to this claim would be

simple shock at the suggestion.

how are logistics handled in every modern army? centrally. how is rationing managed for civilians in wartime? centrally. there was very little difference in the organizational principles of the USSR and the capitalist powers during WW2 except at the production level (who owns & manages the farms and factories).

therefore, deficiencies are not organizational, but from the inputs---which they could possibly claim central planning hindered, it's easy to procure production figures that expose that as a joke---and the obvious answer to soviet deficiencies was the loss of territory and material from the fighting