Crime is committed at a higher rate than in any other advanced nation, though some of the others are catching up.
> The idea that we are soft on crime is insane
Not even a little bit insane. There are a million criminal laws on the books that do not get enforced at all. For example, I live in a state that is stereotypically conservative and "tough on crime" and any marijuana-related products are strictly illegal, most often at the felony level; yet I constantly smell it while driving on the road, no less! People are smoking while driving all the time. This cannot be described as anything but soft on crime.
The US system was overall built by and for people who are largely self-governing. This philosophy gets in the way of a true hard-on-crime pivot.