Actually the second link you provided mentions how private prisons take steps to keep inmates 'in' longer. So that's on incentive.

I haven't taken the time to look into it in detail (so shouldn't make sweeping statement of course), but I do remember hearing in other submissions on this site that prisons lobby and fund elected representatives who are 'tough on crime' and who might send convictions their way, so a truer 'incentive' to incarcerate initially not just keep them there.

I'll see if I can dig those up.