Doesn't the US privatized incarceration so it's basically a _free_ market, where shady deals are made to funnel more public money to private entities, and many

Doesn't the US privatized incarceration so it's basically a _free_ market, where shady deals are made to funnel more public money to private entities, and many people are incentivized to have as many people in prison as possible? In that case, the cost on citizens for incarceration of people shouldn't be taken into account in the discussion around capital punishment because it's another issue altogether?