I agree that the desire to "jine the cavalry" was rampant throughout the Confederacy, not just the TMD.
The last true AR infantry regiment was raised in 1862, whereas mounted AR regiments (the 45th-47th come readily to mind) were raised in 1864. The pattern is exactly the same with LA, TX and MO--infantry only through 1862, cavalry thereafter and up to 1865.
As to policy, I've seen many references in the OR to the high command's WISH to dismount cavalry. See, for example, E. Kirby Smith in OR 34 pt. 2 p. 1043 suggesting to Price in 1864 that he dismount 1/2 of his cavalry.
Another reason to dismount--cost. A cavalry regiment simply cost more money to maintain than a similarly sized infantry unit. Carl von Clauswitz estimated that a (European) cavalry unit of 150 men would cost as much money as an infantry unit of 800 men. The reasons are obvious--the added cost of forage, saddles, horseshoes, accroutrements, etc. Lord knows the CSA didn't have the extra money lying around. And every man kept at home in a saddlemaking shop is a man not in the front lines.