If, I may add two cents. Davis knew there was more of a threat of losing territory West of the Mississippi and that land was more valuable to the Confederacy than Kentucky and Tennesee, when it came to expansion of the Confederacy. So that Territory needed to be protected.

Johnston and Bragg thought the land West of the Mississippi, less valuable than the Territory they were currently defending. Of course with every Commander thinks it is his field of endeavor that is more important than all the others, so troops from Arkansas would not have impacted the end result, according to them that is.