In a very oblique manner it did. Industrialization (which was very much a product of free markets) of the Northern States made the economics of slavery untenable in the North. Once people were not as blinded by profits, they could actually see that slavery was a moral evil. In the South, the economics were very different and therefore a lot of rationalizations were formed as to why slavery was not that evil.
In addition, Industrialization enabled larger population growth in the North as well as larger production. This is what gave the Union the advantage in manpower and material that allowed the North to win the Civil War.
It was actually quite the opposite. Pre-industrialization, serfdom and slavery were basically equivalent. You hand a local lord and if you worked for him you got food and shelter. Your alternative was to run off into the wilderness and fend for yourself, which frequently meant starving or freezing to death or being mauled by a bear. Unsurprisingly not many people chose that.
Then factories show up and suddenly your alternative is to run off and go work in the factory. Naturally many people started preferring to do that, which turned the plantations upside down because their economic system was based on the workers not having anywhere else to go.
Their response was brutal. Chains to keep slaves from running away, hunting runaway slaves with dogs, savage beatings, etc. None of that stuff was really commonplace before industrialization. The response to industrialization was what made 19th century slavery so much worse than traditional serfdom.
But that response was as futile as it was brutish. The factories made slavery uneconomical. You can't defeat supply and demand with chains and whips. All they do is cause the slaves to want to run away more.
The factories destroyed slavery directly, by out-competing it. It's questionable whether the war was even net positive -- that was a whole lot of blood spilled over an economic system that couldn't have sustained itself much longer in any event.
In the South, people's livelihood depending on slavery. Because of that, their minds did all sorts of rationalizations as to why slavery was not that bad.
>The response to industrialization was what made 19th century slavery so much worse than traditional serfdom.
The other thing that made 19th century slavery so much worse than traditional serfdom was the racial aspect. If a serf had some skill and went to a town and somehow became a craftsman, people could not look at the him and know he had once been a serf. Because of the racial aspect, ex-slaves could not escape people immediately knowing that they had been slaves.
Even if say free market solved the issue, is it reasonable to wait centuries for the free markets to solve things then dare to vote some laws ?
It's worth knowing that the south was once considerably richer than the north, but industrialisation changed things in the 19th C, by the end of which the north was vastly richer (per capita), richer than anywhere had ever been before. In this sense free capitalism did vastly outcompete an unfree economy.