The cost may have been high for a slave, but then keep in mind that the divide between “rich” and “poor” was much much larger then. What may have been several years’ average wages may have been pocket change for the owner of a decent sized plantation.
As mentioned earlier, slaves could not testify in court. Unless family members (or white employees) on the plantation were willing to testify, there was no way to prove what happened - especially by the time someone got around to investigating, the body might be rotting in an unmarked grave, in the days before serious forensic autopsies. The “correction” clause obviously gives a convenient out - all the owner has to do is say he was disciplining the slave for some transgression. If he was smart, he’d say it was for something nobody else was around to see.
One presumes that the few cases that were prosecuted were for other reasons - excessive abuse known to the community, actions done in front of too many witnesses to ignore, actions that seemed to cause unrest among slaves, an unusually ethical prosecutor, etc.
The story of “12 Years A Slave” recounts several incidents of slaves being killed, either deliberately or as a byproduct of excessive discipline, at the time when slaves were already valuable property. Assuming this story is accurate and a valid random slice of southern behaviour, it suggests that death by discipline or white viciousness was not uncommon. However, he was dealt to a slaveholder unscrupulous enough to most likely deal knowingly in falsely apprehended freedmen, so may have ended up with the wrong sort of owners anyway. (And in the end - spoiler - the local authorities had no problem sorting out the situation once his white friends became involved.)
To be fair (if possible) the Germans by contrast were dealing with supply and distribution shortages by the time the war was getting close to the end. Certainly there was a divide of viewing some countries as “civilized, like us” (??) vs. as a bunch of subhumans, but the problem was not so much withholding rations as also a choice of distribution.
One commentator on Roman society pointed out that the Romans thought of having sex with slaves, for example, as “very bad form”. If you want to know what society thinks of as despicable, see what the commentators accuse their enemies of. Not that it did not happen, but socially it was not a “nudge nudge wink wink - we won’t talk of it” thing.
Roman slaves were generally captives of war. You either slaughtered the losers wholesale, or you split them up to be used as labour, but dispersed so they could not get together and create more trouble. (Plus, people falling on hard times could be sold into slavery for debt, IIRC - As a result there were some fairly sophisticated and educated people who were slaves. Slaves in many of these cultures were somewhere half-way to indentured servant category. Some could own their own property, even eventually buy their freedom. Presumably, though, on country plantations far from prying eyes and independent witnesses, anything could also happen. As is common in any society, those with power and position were often immune from legal repercussions over crimes against lower ranks of society. (With the warning that such cases provided leverage should political enemies want to pull them down)