Some airlines do request them as part of the hiring process, even if pointless.
E.g My last carrier gave someone a no incident letter, when they were in fact leaving precisely because of a major incident. I remember the fleet manager remarking "well technically it was an accident, not an incident - so we're being truthful in signing this 'no incident' letter..."
They wanted rid of the employee without going through the firing/payoff and battle with union.