The main problem I see is it's more work because there's another aspect of an applicant that needs investigating; an extra step with those with records.
I actually had a convicted killer as a helper for a short time and had even worked for his victim's company in the past.
It was a non issue because we all knew the details of the incident and knew the only person he is a danger to was dead. We didn't need to spend time researching him and there was no nagging doubts about our safety.