You are correct - but the US system is different. The main goal of Denmark's prison system is likely centered around making sure people are reformed when they get out. The loss of freedom itself is the main punishment. The US system focuses much less on reforming people, but instead focuses on punishment. Loss of freedom isn't enough.
Mandatory minimums do have cruel outcomes: Usually the minimums were put in place as a political ploy (we'll make sure those bad people get put away for a long time - to keep your kids safe at night). I'm pretty sure that evidence doesnt' exist - any that does is likely against mandatory minimums.
So the only reason mandatory minimums are not unconstitutional is because of the word 'and'? I guess you can then make any cruel punishment constitutional by making it usual.
Heh. Unfortunately it is more complicated than that. I think the line includes cruelty along with the 'and' to attempt to put some sort of limits on punishment and to make sure the punishments matches what society knows as 'uncruel', though in practice it doesn't work out as well as imagined.
I'm not sure if anyone has appealed mandatory minimums on the basis that they are cruel and unusual punishment: They probably have research to back up their claim. This is probably the true reason they aren't unconstitutional - because you have to appeal and sue (sometimes pretty far) to try to get those turned over. The other option is for the public to pressure legislature into changing the laws, and considering the current climate in Washington, I doubt that is going to happen soon enough.
Mandatory minimums do have cruel outcomes: Usually the minimums were put in place as a political ploy (we'll make sure those bad people get put away for a long time - to keep your kids safe at night). I'm pretty sure that evidence doesnt' exist - any that does is likely against mandatory minimums.