Doyle, what you say about the over-abundant cavalry in the TMD is spot on. Who wouldn't want to ride instead of walk? Plus, a horse could carry more loot than a man, and if your horse died you could get a furlough to go home to obtain another.
All the incentives were for soldiers to want to "jine the cavalry". As well as pre-existing beliefs in the prestige of being on horseback.
I'll throw another thought out there--that in a completely unintended way, the cavalry saved the TMD from conquest.
During the Camden Campaign of 1864, the opposition to Steele wasn't so much the Confederate forces (Sterling Price's cavalry, mostly) as it was the eaten-out countryside. By accident, the Confederates helped create a "scorched-earth" zone in southern Arkansas that prevented Steele from going to Shreveport and linking up with Banks--as Steele himself acknowledged.
I forget who it was, but some military expert described an area as one "where large armies starve, and small armies get beaten". The numbers deficit on the CSA side was so pronounced that something had to be done to redress it. And in the TMD, that was in essence done by denuding the countryside so that the superior Union forces had to either go hungry or advance along blockable river lines.
The CSA didn't consciously create this scorched-earth zone. It was more the result of the ravenous demands of the cavalry, the local farmers being robbed by jayhawkers and refugeeing in Texas, and the general absence of farmers caused by their presence in the army. In any event, it worked out so that the only force the Federals could feed in southern AR was a force that the Confederates could handle.
Could the Confederacy have adopted this scorched-earth strategy in the Cis-MS? We'll never know. Certainly it would have been unpopular with the voters and the public in general.