Heavy cruisers escorted convoys for the threat that might appear

Was using a heavy cruiser largely for anti-aircraft defense an inefficient use of its crew?

No; the cruiser was also there to counter Italian heavy cruisers if they appeared, a risk escorts could not safely ignore.

Escort planning cannot assume an enemy surface force will remain absent simply because it did not appear on earlier runs. Italian heavy cruisers were capable enough that the Royal Navy had to provide a matching counterweight, even when that ship spent the voyage on air-defense work. The escort can look underused only because hindsight reveals that the surface threat never appeared. Arctic convoy experience, especially PQ 17, warns against dropping protection after earlier passages seemed safe. The convoys had to get through, so the contingency force was necessary.