> That's because that distinction is not, as far as I know, actually in the Bill of Rights.
It's a distinction made in the case law, even by strict textualists like Justice Scalia. It's not a weakness of the document that it doesn't spell everything out for you.
> interpreting the bill of rights there is a meaningful distinction between public and private property that you are apparently unaware of.
That's because that distinction is not, as far as I know, actually in the Bill of Rights.