I agree that current prison sentences are too high, many drug offenders don't belong in prison, current plea bargaining practices make a mockery of the very idea of justice by essentially turning a criminal prosecution into a game of high-stakes poker, and it is currently far too difficult for convicts who have served their sentences to reintegrate into society in a positive way.
But your analysis leaves out the idea of deterrence.
Heavy consequences for serious violent crimes like rape, murder, assault, etc. keep those violent crimes from being seen as viable options for resolving disputes by people who have self-interest but little-to-no empathy or ethics.
A free democracy with a prohibition on cruel and unusual punishment, can't really do much to criminals other than attempt to rehabilitate them, lock them up, or punish them financially [1]. Enduring sentences of rehabilitation and financial punishments are probably things that a rational, self-interested sociopath would be willing to endure as the price of being allowed to maim or murder someone who gets in the way of what they want. OTOH the prospect losing a few decades to prison, would probably convince our hypothetical sociopath to try to find a lawful way to deal with their situation.
[1] The death penalty is an interesting and complex topic, and I think the consensus is slowly moving toward ending the death penalty. My view is that it obviously does nothing for rehabilitation, it's not cost-effective at keeping criminals off the streets (it's less expensive to imprison a defendant for life than to do all the legal maneuvering courts and legislatures have found necessary to properly protect the rights of the accused), and its deterrence value is not that great (because it's so expensive, relatively few cases go through the process, and it takes a long time, so the additional deterrence provided versus a life prison sentence is questionable at best). Since life imprisonment does a better job of satisfying those three main objectives of criminal penalties, it should be preferred.
In other words, the death penalty either has to get a lot faster, cheaper, and much more widely applied, or we need to give it up entirely. I think the first path is a political non-starter and fraught with constitutional issues, making the second path the only real way forward.