Think about the other facially neutral rights that accrued to property owners in societies where slaves were owned. And think about the many, many, many societies in the world where slavery exists in fact even though it is not explicitly a legally protected category of property.
If you were to make it possible as an abstract matter for slaves to buy their freedom, then first you have to address the really huge problem that a slave has no legal right to his or her own labor. The master owns that. And the master owns everything the slave would putatively own. So, unless the slave is secretly stealing his or her own time from his master and hiding the proceeds from that where the master cannot find it, and enduring all the risk to person that entails, he or she has nothing with which to buy his or her freedom.
The exception to that would be a situation where the master permits the slave to work for money from other people. But, and this is the gravity of the injustice we're dealing with here, there is structurally no difference between that and the slaveowner just freeing the slave outright, albeit on an installment plan.
Now, setting all that aside, let's imagine a situation where hypothetically some system was required whereby slaves could own their own property, to some degree their own labor, and thus buy their own freedom. To do this the states involved would have to set maximum hours beyond which the slaves could not be made to work by their masters for free. The states would have to establish a minimum wage slaves would get paid. The states would have to prohibit masters from charging the slaves for the necessities of life as a way of draining these resources. And the states would have to prevent any number of other schemes (for example, requiring a deposit from the slave so as not to sell his or her family members) that would also drain these funds from the slaves. Seriously, think about all the different means of duress and coercion available to someone who holds another person as a slave. How could you prevent all of them from being exercised and still have a situation that you would call slavery?
Now, we know from the historical development of labor law in the United States that the right of government to regulate wages and hours terms in contracts between private persons was only truly established subsequent to the end of slavery. Which makes sense in the employment context, because on what grounds are you going to start regulating consensual labor arrangements when nonconsensual ones persist?
What any such "buy-out" system amounts to, because it is dependent on the good will of the slaveowner in so many ways, is as a system of voluntary manumission. And, as we all know from the stories of such slaveowners as George Washington, that was already a possibility in the system that existed.
Of course, there is one additional way this system would run into trouble in a legal system in which property rights are sacrosanct (which seems in the western context to be a pre-requisite for slaveowning societies to exist in the first place). Property rights include the right to decide whether or not to sell the property, excluding only limited exceptions like purveyance or eminent domain. Slaveowners would object to any system that would require them to sell under given circumstances because it redefines what property means. And within the legal context of a conservative slaveowning society, the weight of tradition is on the side of that position. Because once you can require someone to sell one kind of property, what's the limit to requiring them to sell their land or their moveable goods?
In so many ways, it really is simpler and more expedient to just establish the rule that humans are not, never where, and can't be, property.