The fact is that if someone is a rapist, they shouldn’t be allowed to serve time “privately.” They should have to register as a sex offender and all the other jazz in punishment for their crime. Their crime should go on their record - how would it in your plan, since innocent men and rapists are treated the same?
If women are really as scheming as you think we are, then all we would have to do to lock an innocent man up for a long time under your plan is get a bunch of girlfriends to spend time alone with a guy then claim rape in succession. I don’t see how that helps protect innocent men at all.
It is unethical and sickening to suggest that people be jailed without due process. That doesn’t mean the law is perfect or that they are right all the time, but in most cases justice is striven for.