There is a universal that says that object marking that appears on inanimates is more likely than not also to appear on animate objects. The idea that occurred to me for this post originally violated that universal a fair bit, but in an interesting manner.
Consider transitivity and how one can reduce transitivity by demoting an object to oblique status. Somehow, inanimates easily could be considered less 'genuine' participants in an action, and therefore, for instance, mark them by some preposition. We're still really talking about objects though, and what this would amount to would be inanimates marked by prepositions, and animates marked by at most a case suffix.
This seems a bit unexpected. The opposite - animates being marked by a preposition, inanimates not at all - is attested.
However, what if animates triggered a verbal agreement thing, which inanimates did not trigger? In that case, the preposition thing seems like less of a stretch - especially if the animate objects also had some case marking.
So, what happens to other things? Passives - promote animate objects to subjects, leave inanimate oblique objects as oblique objects of an impersonal verb. Antipassives - promote subjects to intransitive subjects, demote animate objects to obliques, leave inanimate objects as obliques.