Sure. It's not something I was formally taught, but rather a viewpoint I came to over time, informed by my own anecdotal experiences and observations. So I don't have any links to share with you, but I'm happy to give a go at explaining my logic.
The naive summary would be that if an individual harms another this is "bad" (a harm to society). To then enact a punishment would be to apply another harm, which would be doubly bad. In my mind, justice is the restoration of balance to the whole, so double harm can never be considered just.
I understand the "goals of punishment" you've outlined and don't even disagree that they can be met (to some extent) via this mechanism. Though I wouldn't classify restitution as a "punishment"[0]. I can also see how the harms from punishment can be moderated when enacted by a state (a group of individuals holding some claim to legitimate power). The question is not whether a system of punishment is sufficient, but whether it is necessary.
If the goal is to reduce all harm to the minimum practical amount we must be pragmatic in our analysis and execution.
I have also seen states grossly amplify the harms involved well past what any individual could be capable of and I have seen individuals operating on behalf of the state launder harm through their office to absolve themselves of any personal accountability for what are ultimately personal actions.
From my observations, those who receive punishment after causing harm rarely become reformed and productive members of society. If anything the punishment[1] leaves them bitter and often actively disadvantages their opportunities for success, leading them to commit more harms and drawing us down a dangerous spiral. Even in confinement these individuals often commit harm to their peers or to those that guard them—and, more abstractly, to the tax payers that are compelled to back this system.
It's not that I doubt these methods can "work" to some extent, but that I see us stuck in a local maxima. I believe we can do much better.
I believe the vast majority of crime that is commited in modern societies could be eliminated through better education, cooperation, and social equality. Why commit crimes, especially violent ones, when the opportunity cost of not pursuing more productive activities is large?
For what remains, I would propose applying insurance. When the volcano erupts and the magma damages my house I do not feel the need to "punish" the volcano.
I do believe there is a floor to violence (and other criminal acts) that will exist no matter what we do. (One-off crimes of passion or acts commited by the criminally insane, for instance). For some of these there may not be any better answer than imprisonment or exile in order to protect the community from future acts. However, I'd love to explore the proactive solutions I recommended above (education, equality, etc) and leave the shrinking vestiges of the current system to handle these edge cases if necessary.
[0]: Likewise, I can see the utility of—e.g—restraining orders and would not call those a "punishment" either, though in this we start to get into the grey area of restraint (limiting an individual's freedom of movement could be classified as a harm).
[1]: Excepting the ultimate punishment.