But why is that a useful definition of ownership? It doesn't fit any of the desirable properties of a useful definition, in my opinion. It provides no explanatory power. since other definitions like mere possession or just happenstance describe the state of the system equally well. Better even, since they don't rely on a theoretical capacity, dependent on shared moral understanding with other agents to describe that property.

The difference between mere possession of a thing, and the ownership of it, is tied up in the capacity to exclude other moral agents from the use and enjoyment of that thing. Therefore, insisting on the idea that we "own" ourself in the first instance, as matter of natural law, in the unitary person thought experiment, yields no useful explanatory power for what property even is. It's just messy philosophical reasoning.