Chastity belt instead of prison for rapists?

Wouldn't this be a fairer solution? Something like this: https://www.amazon.com/Bondage-Shop4u-Male-Chastity-Belt-Cage/dp/B00BPN2C4I but more highly-secure. What are you thoughts? Would this help solve prison overcrowding? Would it allow the rapist to receive a deterrent punishment while avoiding getting institutionalized?

>>10
You can rehabilitate person with psychiatric problems by placing him among career criminals. Pedophiles become pedophiles because of their brain organization, not because of social factors. And other crime has social factors, like low education, low income and culture of crime. If you rape pedophile in prison, it wont fix him, but likely make more violent, and on release he is more likely to rape and kill his next child victim.