“The South remained a predominantly agrarian economy while the North became more and more industrialized.”
To be a bit more accurate, the South failed to adapt to changing technology.
If the south had gone “industrial”, adapting to changing technology as you suggest, the north would’ve starved to death...
Tough to do when wave after wave of armies come marching into your land killing your people and destroying your stuff, and eventually evaporate 4.5 billion dollars of all the assets you had spent your life building up.
If people had left them alone, there is a very good chance that the "technology" would have developed in the South.