We, as a nation, elected "tough on crime" politicians. As you already pointed out, the private prisons lobby. They lobby the politicians we as a nation elected. We have a democracy, we vote for tough on crime politicians. As a result, we imprison lots of people.
This is propaganda designed to legitimize the actions of the individuals who are effectively using coercion and violence to enslave large parts of the population.
If "We", as a "nation", elected pro slavery politicians, it wouldn't justify the owners of land and capital to enslave people.
This would be the moral equivalent to a belief that some religious groups hold: that "We" are all born sinners, we all deserve to go to hell, but by the grace of god (the state), we can repent (vote) and accept the next savior (presidential candidate).
Democracy, as you call it, is a religion based on the belief that elected groups of individuals have legitimate authority to totally violate basic human rights. In this case, an individual right not to be enslaved.
But, in reality, nobody has a legitimate authority to enslave another person. Voting is participating in the delusion that the state has legitimate moral authority to imbue unrighteous people with righteousness in the first place. They don't.
It doesn't matter if "well, we voted for it": the politicians, executives, as well as the employees and shareholders of these "sanctified" corporations are still morally responsible for their actions, and should be held accountable for their actions.
I partially agree that we do elect "tough on crime politicians" and we get what we elect. But part of the problem is that we also live in a reactive society instead of a proactive one. We react to incidents with tough laws that sound good when emotions are high and in the moment. Yet we fail to consider the long-term consequences of those laws, so 5-10 years down the road we face the real results of the law. We also live in a society where it is easy to be lazy with laws and take a zero-tolerance approach. I would characterize it more as we have "tough on crime politicians" who don't start that way, but over time become that way because of lobbying efforts and reelection campaigns.
If government policy doesn't have a strong positive correlation with the desires of the population, then you can't just write everything off as "well, we elected the government."