I believe I've read on the forums that a BC's two primary functions are as a replacement for the in game manager and as a support coach to the other two coaches (as in the BC's other ratings also affect player development). Does it make sense to punt the strategy rating for a BC and hire the best possible PC or BC (maybe split HC and PC in BC roles every other level and stash your prospects accordingly)?

To he best of my knowledge, no one has ever verified that the other attributes of the BC have much effect. I used to pick bench coaches that would help with whichever other coach at that level (BC or HC) was lower rated. Now I honestly do not spend that much time on coach hiring. YMMV.