One of the best tenants I’ve had was a freelancer. We talked about what he did, I was convinced that he actually knew what he was doing, and we signed a month-to-month lease on trial basis after calling his references.
No employment verification requested, and I think I did the guy (as well as myself) a favor by being flexible.
Didn’t do a background check either. I feel that anyone who’s paid their debt to society shouldn’t be under disability for life. I did Google his name to see if anything particularly heinous came up though.
BTW – the hole in your idea of large firms doing background checks, is what if something happened AFTER s/he was hired?