Not only is that true, but the first R is also the one providing the least value to society, aside from sating the vengeance-lust of generally uninvolved parties.

When I said values I didn't mean "value" as in "benefit" but moral values (which in the US were heavily shaped by Puritan Christianity). Vengeance is a part of that, reimbursing the victims for their suffering by punishing the offender (and thus making them suffer "in return").

As an example, in capital punishment allowing specifically members of the families of the victims to sit in on an execution is solely based on vengeance. Neutral observers, sure -- to document it. Relatives and family, sure -- to allow them to say goodbye. But the victims' involvement ends with that of the judges. If it weren't for the aspect of vengeance, the execution would be "not for them", it's just carrying out the sentence.