I think you give BB WAY too much credit/blame for who he has to play with. I heard on radio, on two different programs, that he is determined to be rid of Dessens as soon as he's given an opportunity by the GM, and just this week heard that JoeBlows has 'finally agreed.'
I bet it is the person whose ego is riding on the personnel decision - in this case Nincompoop with his two-year contract to Dessens - who insisted they stick with Dessens a bit longer. Note, GM's job is not in danger because of Elmer's failings, so it's not as pressing for him to act fast; if Elmer straightened out, Joe would look less incompetent.
You listen to BB in interviews or watch his face during Elmer's outings and he is plainly fed up, and has been for two weeks. But he doesn't HAVE the right guys in the pen to do what Gil Hodges did, even if he wanted to. And he can't call Tucson and say, "Send me Good, Service, and Bruney. You're taking Oscar, Mantei, and Choate." He has to persuade the GM to move guys up and down and out to suit his needs, and it may not be as simple as ordering fries at a drive-through.