No, they're calling Alligator Alcatraz, because they think Alcatraz was a decent place. HitlerPig has even floated the idea of re-opening it.
Alligator Auschwitz is too close to reality, and they are still in the denial stage that they are following the Nazi playbook.
The bottom line is that they want to incarcerate as many people as possible.
What does a corporation do when they are already paying their people as little as possible, and replace as many as they can with AI? Imagine if slavery were legal, and they could force people to work for literally free?
The only legal form of slavery is prison labor, ensconced in the Constitution, so as long as people are in prison, the administration can rent them out to wealthy corporations. The corporations get cheap/free labor, and the government gets to maintain control.
In addition, that's how they will treat people who require any public assistance, like Medicaid or Food Stamps. You will be forced to live in a camp, and work for whoever they tell you to work for. In return, you will get a bed, basic food, and minimal medical care.
Same with homeless people. Put them in a camp, force them to work, and declare the homeless problem solved.