First off, there is no single "US prison system." There are 50+ distinct prison systems in the US (one for each state/territory, plus a federal prison system) as well as hundreds of "jail" systems which are distinct from (and run by different folks) the prison systems. And that doesn't take into account the private prisons or the immigration detention facilities.
Secondly, there's wide variety in how these disparate systems are run, funded and used. As such, it's not really useful to talk about the "US prison system" as a monolithic institution.
However, one current runs through most prison systems in the US -- cruelty and a lack of interest in rehabilitation.
What's more, those who have been incarcerated are generally discriminated against (lack of access to jobs, housing and reintegration back into their communities) by society once they've served their time.
And that's the biggest cruelty of US society against those who have been imprisoned. And it negatively affects the economic potential of those folks, as well as the economic well-being of their communities. Which may lead to recidivism.
By focusing on rehabilitation and not continuing to punish those who have been incarcerated after their release by discriminating against them in a whole host of ways.
That's not to say there aren't folks who are too dangerous to be allowed to live in society. There certainly are. But those are a tiny fraction of those who pass through the various carceral systems in the US.
We're doing it wrong and have been for a long time. We can, and should, do better.
Edit: Fixed prose.