That would not work. I do not want my teenage daughter to do part time work in a business that employs a sex offender. I do not want to work with an insurance agent who engaged in a financial fraud few years ago.
Is the answer to not allow any sort of background checks? I would say no, but it also seems like there is a lot of room to improve our current system and find it in our societal heart to not perpetually punish a person for a past minor offense.