I have played three LGB games recently, with six of us as CCs and one of the CCs also playing the role of CIC. There are three ways for a CC to obtain cards to replenish his hand.
Throw 2 sabres on a CC Initiative Roll (high odds)
Play a Scout Card
Play a Command Card with 3 Stars (and not use the march moves)
So it soon became clear that the way the CIC plays his hand is critical in giving the CCs the chance to keep replenishing their cards. Sensible choosing of cards from the Courier Rack and the distribution of the cards he has available in his CIC hand is all important. I think its another great aspect of the LGB games, a poor CinC will let his commanders down badly!