True, but there is this mythology that all prisons in the USA are private prisons controlled solely by corporations, which is wildly untrue. Public prisons aren't much better than private prisons, due to the fact that they are just punishment and not rehabilitation.
On your second point, undocumented immigrants also count in the census and give more weight in representation and elections, even though they cannot vote. In a perfect world, we would expect elected officials to represent all of their constituents, not just those who voted for them, but we are far from that.