It would contribute to the system that is perpetuating these kinds of injustices. Recall that a good portion of these people serving life sentences for non-violent crimes are in state prisons. How is helping them build their software systems going to find justice for a man in jail for life for stealing some tools?
By the way, this is not a rhetorical question: I'm honestly trying to understand this point of view.
1. In the courtroom. These people could have received a faster, more painless, and more just trial. The proceedings could have been more open, easier to search and data mine, and hence easier to react to faster. Additionally (and somewhat science-fictiony) I personally would like to see us experiment with alternative juries - particularly much larger, distributed juries. If justice can't be crowd-sourced, then I don't know what can.
2. In the legislature. Although the creation of bills is an intensely collaborative process, too often the details are delegated to underlings, and those details are seriously misinformed by the facts. So one piece of software that is needed world wide are better document collaboration tools that are tied to accurate sources. The legislature in particular should be obsessively concerned about how the justice system is applying their laws. Better visibility into what's happening, in real-time, would make the legislature a) more aware and b) more responsive to injustice.
Consider: if we can write the software that cities, states, and even the federal government uses to do it's job, then we can also have a material impact on transparency, usability, etc for the users.
Take the judicial system. It is badly underfunded, especially in California, which has the largest civil court system in the Western world. What if an enterprising group of civic minded programmers simply wrote awesome, free, open software to run a state courtroom, complete with a self-help web interface?
Such a project would not necessarily be fun. But it would be useful, and it would arguably contribute greatly to society.