I am not so sure that easrtern Mississippi and Alabama were militarily important enough to justify their occupation, much like Southwestern Arkansas, Oklahoma, and Texas.

The army to beat politically was Lee in Virginia. The occupation of the Mississippi valley was to cut off his supplies (The Anaconda plan) and tie down re-enforcements, like Hood's Texas Brigade, from the west, and to eat up and tie down the Confederate resources needed to supply the AoT and others from getting to Lee. The Mississippi valley war had no other real military purpose than that.

After those purposes where accomplished in July 1863, the Mississippi Valley war from both a Union and Confederate standpoint stagnated.