The war didn't just happen. It didn't start out as a war to end slavery, either (that happened later, with the Emancipation Proclamation).
As for prison labor, most of the cost of that is borne by the taxpayer, not the company using their labor. Keeping people prisoners in the US is very expensive.
Nothing you just said supports that slavery ended because of the "free market".
1) The Civil War was absolutely about slavery. Here's a professor at West Point talking about: https://youtu.be/pcy7qV-BGF4 (and PragerU is a very conservative source too).
2) The Emancipation Proclamation didn't end slavery. It ended it in states that were still rebelling. It took amendments to the Constitution to end slavery once and for all.
3) I agree that keeping prisoners is very expensive in the US and that most of that cost falls on the taxpayer. But it is very much still (essentially) slavery that the "free market" uses.
As for prison labor, most of the cost of that is borne by the taxpayer, not the company using their labor. Keeping people prisoners in the US is very expensive.