I agree with everything you and Art say. The problem was "public opinion". Armies are a reflection of the society they are drawn from, and in this society men wanted to be in the cavalry, not the infantry. Esp. the new regiments raised in 1864 in the TMD.
Dismounting the surplus cavalry was and is, as you point out, the proper "staff college" response the government should have made. However, many officers at the time thought that men wouldn't volunteer as infantry, and if their horses were taken away they'd desert. The idea was--better the men remain as ineffective, forage-eating cavalry, than lose their services altogether.
Perhaps the officers were wrong. Certainly the dismounting that created Walker's division went more or less successfully, so it could be done. But the feeling must be acknowledged.