I think that incarceration isn't necessarily problem. It's who gets incarcerated for what, and how many innocent people mistakenly end up railroaded. Alternatively, cases of affluenza and individuals who help keep the broken system going, are often considered above the law.
Violent offenders should be locked up. All of them, regardless of wealth or connections. But they still deserve to participate in a fair and just legal system.
Nonviolent offenders should be fined, and the amount they're fined should be equivalent to the crime they've committed while taking their own wealth and ability to pay into consideration. If people commit a very serious nonviolent crime, but either can't or won't pay off the debt they're fined, they should have the option of volunteering in their community to pay off their debt. If they fail to pay fines or repay their community via volunteer time, then potentially they should have their wages garnished.
Most importantly though, nobody should be getting insanely wealthy via investments in private prisons. There should be no incentive to simply pack as many people as possible into a prison while pretending that you've done something positive for society that also just happens to greatly increase your profits.