Are Americans too obsessed with punishment and too unsympathetic about others?

Yes.

The most important thing about prison isn’t vengeance on the transgressor. Punishment is a factor and a deterrent, but it isn’t the point of jail.

The No. 1 function of prison is to keep dangerous people away from the general population. Physically dangerous first, and then criminals who would rob and steal or otherwise harm other citizens.

When someone is released from prison, if they go out and commit more crimes, the prison has failed in its No. 1 function.