People working at prisons have no incentive to be kind or instill any kind of humanity in their actions, thus I would expect having them go through their list of prisoners and determine when prisoners should be released to have just as cynical a result as relying on broken software.

I don't understand why that's your default presumption. Although I don't have any data about this, my impression is that generally people are aware of how long their prison sentences are and are released from prison when they are supposed to be.

This is a matter of administrating the law. If they're unwilling to do their job, they shouldn't have that job.

I am skeptical if the law has anything to do with the people employed in the day-to-day operations of the US prison system.