Van Dorn was the one that named the forces under McCulloch and Price, combined under his command, as the Army of the West.

As far as I can tell, McCulloch's brigade was an independent command before the establishment of the Trans-Mississippi District on January 10, 1862. At least, his reports were addressed directly to Gen. Samuel Cooper, Adjutant-General, at Richmond. Price's Missouri State Guard was ostensibly subordinate to the Governor of Missouri. Pearce's Arkansas State Troops "division" was subordinate to the Governor of Arkansas. Likewise, Pike's Indian Territory command reported directly to Richmond.

When the Trans-Mississippi District was established, all of these feuding factions were brought under a single commander, Van Dorn (less Pearce's division, which was mustered out of service back in September 1861).

I suspect that Heth and Bragg, knowing that the big action was going to be east of the Mississippi, felt that commanding the Trans-Mississippi was like being sent to Siberia. In an era when generals' egos were as large as their beards, it would have been unbearable to be shunted off to a "sideshow of the big show."