The British and French colonial empires, the United States, feudal Western Europe, the Abbasid Caliphate.
In none of those cases was slavery ended because free labor was more efficient. The British Empire ended slavery in its colonies because men you deride as "religious kooks" convinced enough British people that slavery was morally wrong, not because they convinced people that slavery was economically inefficient. Period British people who made an economic argument argued for keeping slavery. Slavery ended in the French colonies because enough Frenchmen came to believe that the humanist ideals of liberte, egalite, fraternite applied to all people, not because they convinced people that slavery was economically inefficient. Period French people who made an economic argument argued for keeping slavery. The northern states of the US ended slavery because more "religious kooks" convinced enough American people that slavery was morally wrong, not because they convinced people that slavery was economically inefficient. The southern states were forced to end slavery because they lost a war to preserve slavery, not because they were convinced that slavery was economically inefficient. Serfdom was ended because enough people were convinced it was morally wrong, not because they were convinced it was economically inefficient. The Abbasid Caliphate did not abolish slavery.
Feel free to provide any example of any society in history that replaced slavery with free labor because slavery cost more.
Except, you know, the way the South fell behind the North in industrial output, becoming instead something of a cotton colony. It's an obvious and logical inference from the evidence.
You have provided opinions and assumptions, not evidence with clear and logical inferences.
You stated that slaves lacked freedom of movement - if by that you mean slaves could only legally go where their masters allowed them to, then we are agreed, If you mean something else by the term "lacked freedom of movement", then you need to explain what you meant. You then claimed that this lack of freedom of movement consumed a lot of time and limited slaves productivity, providing no evidence to back those opinions. You then claimed that the slave system "required individual slavers to take a lot of care for their slaves", which is clearly wrong, from which you reached the unsupported conclusion that slave labor cost more than free labor. You also stated "there was a competition for who could buy and afford more slaves". While this is true, you then made the unsupported claim that this competition slowed down slaves' productivity. You then said that slaves did not make good workers. This is also true, but not because any of the assumptions and opinions you gave - slaves knew that working harder would never make life better for them or their children. You also reached the unsupported conclusion that slavery made industrialization far more costly and the obviously false conclusion that slavery was ended because free labor cost less.
As a whole, the slaveholding states did fall behind the free states in industrial output, but to infer that this was because slaves lacked freedom of movement is not an obvious or logical conclusion. The Deep South favored growing cotton because it was more profitable than industrializing, but Virginia was one of the most industrialized states in the country. Sadly, slavery was sustainable, not just in agriculture, but in industry. Slaveholders looked at the lower labor costs and assumed that meant slaves were more profitable, ignoring that slaves were also less productive. When Hinton Helper tried to show that the slave labor system was less efficient, most white southerners refused to believe him. Even if they had realized that slavery was less efficient, almost nobody was going to voluntarily give away valuable property, relinquish the control they had over their slaves, take the risk of black retribution, or risk a society where a black man could be equal with a white man. The few exceptions did so because they found slavery morally repugnant, not because slavery was economically inefficient.
The patronising imperialist views of that religious kook are irrelevant because the British Empire only listened to him because it saw the Haitian Revolution, wanting to prevent that, and saw that slavery was slow and inefficient in production during the early decades of the Industrial Revolution. Even then, Wilberforce wanted to abolish slavery because he thought that way Protestantism would have spread more rapidly in the British colonies (he wanted them to remain fully subjugated, so much for his supposed high morality). What does a rapid spread of Protestantism mean? Efficiency and lack of costs. Even Wilberforce wanted slavery out due to being more economical without it.
Feel free to provide quotes by Wilberforce or other British abolitionist where they opposed slavery because it was economically inefficient instead of because slavery was morally repugnant.
Yes, I know that the glorious Haitian Revolution abolished slavery because the Haitians wanted full freedom, but the reason why Haiti managed to retain its independence was precisely because the lack of slavery allowed the Haitians to organise in such an efficient way that they prevented the Spanish in neighbouring Dominica, and the French, from ever retaking Haiti. Had the Haitians remained with slavery, their military wouldn't have repelled the French and Spanish (and I think the British as well, though I'm pretty sure that's not the case) forces trying to recolonise it.
Your example makes no sense. If the Haitians had remained with slavery, they would not have revolted in the first place. The Haitians rebelled because slavery was morally repugnant, not because slavery was economically inefficient. The Haitians kept their freedom because death was better than being re-enslaved, not because slavery was economically inefficient.