As with all things the "official" reports do not contain everything. The point has been made that once Hindman was replaced with Holmes, Shavers was without a supporter. Hindman wasn't the most liked personality either as his record of commands show. I suspect that Shavers independent personality and tending to speak his mind freely was much the same as Hindman's and had much to do with his lack of promotions.
As we all know that Politics within the military structure in both the north and south was more important than military abilities.