I am of the opinion that 'punishment' is often several concepts linguistically bound together. It can be for the benefit of the punisher...that is, 'revenge',or it can be for the benefit of society, that is, 'a learning process in which it is hoped the transgressor will decide not to 'transgress' again.....or, it can be for the benefit of the transgressor, that is, 'an unpleasant enlightenment about which behaviors are to be preferred and which avoided, leading to a better life'....and it can of course, also be simply way of ensuring the transgression cannot be repeated....death, castration...etc.

It is not always easy to determine in a specific case which is being employed, as motivation is not always clear...even when stated.."This is gonna hurt me more than it does you!"

Simple punishments can often be effective for simple transgressions.."3 little kittens have lost their mittens, so they shall have no pie!"...so they are more careful with mittens in the future, because they LIKE pie.
But obviously, both the motivation for and application of, many punishments are highly suspect, and until we are better able to sort out what we actually intend to accomplish, it will continue being a source of dispute.