"Well we will never know because it didn't happen that way. The Sothern cavalry was no doubt better, but cavalry could not take and hold ground. Trying to fight cavalry against the infantry and artillery of that time would have found the cavalry slaughtered."
There are two things about that: cavalry has often been used against infantry, though best used not in a frontal attack (as at Balaclava). A cavalry attack on the flank of a line of infantry can roll them up like a venetian blind. Then, even inferior infantry can succeed in their attack.
That's how the British prevailed at Sobraon in the first Sikh war.
The second thing is that cavalry in the WNA outraged the purists by moving light artillery at high speed to support themselves. This gave them more capability against dug-in infantry.
"If the North had just used its massive troop superiority to start off with, the South could not have stopped them."
The South was always outnumbered. Numbers aren't everything. Look at Rorke's Drift.
Tell it to the Germans on the Eastern Front.
PS: And Custer at the Little Big Horn.