You are honestly overcomplicating it. It's not a psyop, it's marketing and PR. Evil is terribly banal; it doesn't take mustache-twirling villains, only average people who are willing to do whatever they need to do to avoid being in trouble themselves.

They need "Alligator Alcatraz" because Republicans figured out 25 years ago that a catchy name goes farther than anything more serious. It is why "Obamacare" is still reviled to this day, despite near unanimous support for the ACA. Nancy Pelosi shutting down Walz for his "weird" label was perhaps the biggest unforced error in political history.