I am curious by what logic is it determined that frequent flying reduces risk
I don't think that it is frequent flying itself that reduces risk. Rather if you fly frequently, the airlines consider you a better customer. Since the airlines want to keep their better customers, they try and make life easier for customers by reducing the airline related "hassles". The airline related hassles don't have anything to do with risk. What some airlines also do is sponsor their better customers for the TSA Pre program, which does reduce risk. Risk in TSA Pre is reduced by background checks.The cost of these checks theoretically covered by the application fee that the airlines pay on their customers' behalf.