Interestingly from an ecological standpoint you are absolutely right. The same goes for sociopaths. Each represent a variant brain that is no longer useful or necessary in our gene pool. Execution though is practically immoral as we do not have the genetic or psychological pedigrees to objectively judge and carry out such a solution. Concurrently our only option is our current path. Expose to society and let social evolution take care of the rest . If we can convince our shared human conciousness of this issue we can establish significant selective pressure against these and other dangerous variants. The reason they are prevalent now is due to an aristocratic counterculture which opposes our naturally developed codes of empathy and rewards sociopathy, pedophilia, and several other maladies with increased social precedence and thereby genetic heritage. Edit: To specify, we do have the psychological pedigrees to convict and execute based on provable crimes. What I am referring to is genetic elimination via screening. A few years ago I designed an experimental method to objectively identify degrees of sociopathy and psychopathy via dream amnesia and neural-link simulations. That is, put a mind under hypnosis and use a brain implant to design a series of dreams which test parameters of empathy/sociopathy (willingness to commit theft, rape, murder). Using a large number of simulations (400+) a precedent or scale of executable natures could be established. This means through simulation we could judge and execute sociopaths before they have committed a crime by a morally reasonable method. This is like pre-crime, but could become logically and morally sound with the proper basis of data. Sadly as with all precedents such a design could be easily exploitable by an already sociopathic aristocratic culture.

We need to bring back hanging. Simple. Breed them out of society.

I think you're showing too much generosity towards pedophiles. Pedophiles skulk in corners, like cockroaches, knowing exactly the harm they're doing to children. When they talk about their 'love' for children, they have no idea what love is. Love is wanting what is best for the person whom you say you love. If these pedophile monsters wanted what was best for the children they supposedly 'love' they would never groom, sexualise, abuse and rape them. I don't believe pedophiles have a mental illness. That's insulting everyone who has had a mental illness like depression, anxiety, BPD, schizophrenia. These pedophiles are narcissists, meaning they can think only of themselves; it's all about them; they don't have the capacity to empathise with or love anyone. They are sociopaths and psychopaths, who either love seeing children suffer or don't care that the children they're raping are suffering and will suffer for life. Narcissism/sociopathy/psychopathy are not mental illnesses.