An alternate hypothesis by Stephen Thomas of Harvard Medical School is that medicine has been getting so good that many crimes that would have been murders in a previous era are becoming attempted murders.

http://people.wku.edu/james.kanan/Murder%20and%20Medicine.pd...

  Despite the proliferation of increasingly dangerous weapons 
  and the very large increase in rates of serious criminal 
  assault, since 1960, the lethality of such assault in the 
  United States has dropped dramatically. This paradox has 
  barely been studied and needs to be examined using national 
  time-series data. Starting from the basic view that 
  homicides are aggravated assaults with the outcome of the 
  victim’s death, we assembled evidence from national data 
  sources to show that the principal explanation of the 
  downward trend in lethality involves parallel developments 
  in medical technology and related medical support services 
  that have suppressed the homicide rate compared to what it 
  would be had such progress not been made. We argue that 
  research into the causes and deterrability of
  homicide would benefit from a “lethality perspective” that 
  focuses on serious assaults, only a small proportion of 
  which end in death.

As for whether governments should focus on prevention rather than punishment, it can also be argued that incarceration does indeed prevent recidivism during the period of incarceration.