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?

Castration only reduces chance of a christian reoffending and attacking another child by about 50%. Chastity belt doesn't even reduce sex drive, so the sexually frustrated priests and believers would just use limbs, objects etc. to molest children, probably at a higher rate than castrated christians.

Prisons are overcrowded because people involved in petty crimes are thrown there.
Stop locking people up for doing drugs and you'll have enough space for all the rapists.