I'm no expert, but I think the reason they built Guantanamo in Cuba is so it's away from any legal oversight. And I also assume that this doesn't come up in debates because it would instantly by followed by accusations of being soft on terrorism.
After 9/11 there was this perception (somewhat engineered by the neo-cons, but also organic in that Americans had never experienced anything like that and had a bit of an existential crisis) that American civil liberties and laws had actually made the country weak and had created a loophole that terrorists had been able to exploit. This led to the "new normal", where it was seen as necessary (even a matter of civic duty) to accept ceding our civil rights and liberties in order to allow the government to aggressively pursue the terrorist threat by any means necessary.
This lead to Guantanamo Bay and the normalization of indefinite detainment and torture in American culture, to the increased militarization of American police, to the modern global surveillance panopticon as revealed by Snowden, and the War on Terror.
It's not. Both Cuba and the United States recognize that Guantanamo Bay is part of Cuba. They disagree about whether a pre-Revolution lease agreement is still in place or not.
Obama's efforts to close it, which did come up in debates (and came back in 2016) were basically rebuffed by Congress. Not because they want to keep Gitmo open, but because nobody wants the prisoners moved into their constituency's backyard.
Damn, if there are people so dumb that they would buy "I'm not talking about the general case but just this one dude that we KNOW was sent there BY ACCIDENT - can't we just release the poor guy?" as being soft on terrorism then it's no surprise US politics are such a shitshow...