Have punishment and incarceration become too intermingled?

Avoiding a hijack of this thread towards the end:

I think society is served by punishment for crimes by alleviating people’s desire for revenge. I think incarceration is meant to protect society from continued criminal activity. To me, both concepts are important, but we often seem to combine the two, and lose the distinction. Am I off base here?

There are a number of things to consider when deciding how to treat a convicted criminal:

Punishment: penalty for violating norms. Even if we know for certain that someone will not re-offend we have to do this to show that society does not accept certain behaviors and they have consequences.

Personal Deterrence: stop them from doing it again because of the consequences they faced.

General Deterrence: stopping others from committing the crime.

Public Safety: locking them away so they can not commit more crimes.

Rehabilitation: changing their behavior so they will not re-offend.

I am sure there are others as well.