I am sorry for your pain.
A pedophile is someone with a sexual attraction to children - pedophilia.
Interpol (PDF, see page 86) has recommended against using the term "pedophile" to refer to sexual abusers, because it conflates
pedophilia, a mental health condition, with behavior.
Those with pedophilia
do not often abuse children, and those who abuse children do not usually have pedophilia (only one-third do). So, in addition to being a recommendation from Interpol, conflating "pedophile" with "sexual abuser" spreads myths about the reality of sexual abuse, and of pedophilia. This can push those with pedophilia away from help, which can enable abuse rather than prevent it.
Most *abusers* do not go on to commit another sexual offense, they typically commit probation/parole violations, if anything at all. The statistics, DOC reports, and studies all indicate this, while they may vary slightly by location. So it is not jail for life or death. Here in Minnesota, for example, the sexual recidivism rate is 7% with a 3-year follow-up period, and the MN-DOC who did the report only looked at those released from prison where many sex offenders are given probation.
In short, recidivism is not the biggest contributor to sexual violence, first-time offenders are, and 97% of sex offenders have adverse childhood experiences in their backgrounds. One obvious answer, if most sex offenders have trauma in their childhoods, is to provide mentoring and appropriate mental health care for those who experience trauma during childhood. However, mental health interventions are not terribly popular with parents or schools. So how could these populations be shown or convinced that they are a good thing?
That is one perspective, but I doubt you will win much of the world on the idea of preaching Jesus to at-risk populations until they turn to God. Most abusers are religious, so clearly religion is not going to be an end-all solution, nor is it ethical to ignore the need of those with mental health issues to preach at them.
As far as brain screening goes, we have mental health surveys/screenings already that can identify if someone might benefit from therapy. We also have ways of using fMRI to study people's arousal patterns, even without their awareness. Are you suggesting we use these tools against people's consent?