My answer is Yes; save the State monies but, more importantly to protect the undermanned prison guards who are doing their jobs plus overtime whenever needed.
Solution? Privatize the prison system.
No. This may be a bubble; the root causes need to be examined and a complete review of the laws that are driving the majority of incarcerations - if any of them legitimately should be changed, then change them. Furthermore, by adding additional staff you are adding much more expense than overtime. Health benefits, pension, etc.
They need to change the reasons people are sent to jail.
Drug laws should be re-examined.