I believe that the reason that men late in the war wanted to be Cavalry or mounted Infantry rather than plain Infantry is far simpler that the makeup of society. I believe that by 1864 men simply wished to ride a horse rather than walk 30 miles a day going to a battle. Wouldn't you, if you could?

But from a management standpoint of the Army General Staff, as has already been pointed out with any mounted service Cavalry, Mounted Infantry, or Artillery, you lose 25% of your effective force just holding the horses.