Americans are not a mature people. They find it scarier to be without a gun than to be without a doctor.
Their mentality on crime is that they wanna punish bad guys. They don't care about justice, they just wanna "fight bad guys" like in an action movie. We can see this in how they obsess over Lindsay Clancy. They don't care that she has psychosis and would be better served in a mental institution, they saw that she did something bad and they wanna see her punished.
The reasons for her actions are not important, the fact that there's a better solution is not important, the fact that Not Guilty By Reason Of Insanity doesn't mean she gets to go home is not important.
She's a bad guy, and bad guys get punished.
Americans favor punishment over rehabilitation not because rehabilitation doesn't work (Other countries that focus on it show that it definitely does), but because they are immature and care more about "Fighting bad guys" than actual justice.