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?

Because the main purpose of prison isn't to prevent future crime. It's punishment.

Also as a practical matter, people will start raping more if they knew they wouldn't go to prison for it. Wearing a chastity belt isn't so bad compared to completely losing your freedom for N years.