Howdy,
If the Confederates had stayed in Arkansas how could they have continued to support and supply their army? By this time of the war Arkansas had been stripped of just about all of her resources. All union supplies had to be brought in from out of state.
I doubt the Confederates realistically had an option to stay and operate in Arkansas. If so, the question became in which direction to move, and how? Unable, or unwilling, to cross the Mississippi River as authorities in Richmond directed, Missouri was the only logical choice. Price probably was not the best choice for command, but was selected because he was from Missouri. He failed miserably. The decision to move into Missouri was probably made out of pure desperation as the war in the west had already been lost.
A more viable option might have been "hit and run" raids to capture critically needed supplies without substained engagements, but they would have had little strategic value to the Confederacy.
Bobby