Does imprisonment reduce crime? Yes.
Do many crimes cause considerable harm and hardships to victims? Yes.
Does America imprison too many people? In light of my answers so far, you might expect my response to this question to be no. But it is a strong yes.
Imprisonment reduces crimes against the general public, if only because of the incapacitation effect; that is, people in prison cannot commit crimes against the public (they can and do commit many crimes against other prisoners). For certain crimes, imprisonment is also a deterrent, so that potential offenders are kept from committing crimes by the prospects of prison terms, especially when there is a good probability of being caught.
On the other hand, imprisonment also raises the likelihood that some prisoners will commit crimes when they are released because their skills at legal employment eroded while in prisons, or they learned in prison how to be better criminals, or they become blacklisted for certain jobs, or other reasons. Nevertheless, a study on the decline in crime by economist Steven Levitt, along with other research, finds that on balance imprisonment reduces crime. The main disagreement is whether the whole effect of imprisonment on crimes comes from the incapacitation effect or whether some is also due to deterrence. I believe deterrence is also at work.