I can only quote advice relating to industrial/ commercial (non-banking) corporations, where I believe a lower level of control may be considered appropriate. ..... When I worked in external audit (big eight firm, sorry, big six, .... five, ... four, is that right?

), our clients were expected to open all mail under dual control at all locations where invoices and checks were expected to be received, and to log all significant items.
Later when I worked in insolvency, it was routine practice to log all mail received (no payments were routinely received, so no dual control was necessary).
Like any business management has to accept a level of risk they are comfortable with. With checks being received from clients I wouldn't be comfortable without dual control.
BTW Dual control, in my mind at least, doesn't mean two people have to be focussed on the task; another person in the same room, with the person dealing with the mail in plain view (not facing the wall, or inside a "cube") would be satisfactory.