I’ve read that the magnitude of punishment has less of a deterrent effect on crime compared to the certainty of receiving punishment at all. Softer consequences that you will probably face, as in parts of Europe, are different from harder (on paper) consequences that you will likely escape under a progressive prosecutor in the US. See the Chicago, San Francisco, Milwaukee, and Baltimore DAs for examples of this.

Edit: And don’t confuse American police/law enforcement, who are often harsh to say the least, with the legal arm of the criminal justice system. In many US cities the two are often at odds, as lax prosecutors and DAs release criminals almost as soon as police apprehend them. The Washington DC Chief of Police in particular complained about this recently.