Viruses don't work that way. They enter the nose and either enter and infect cells somewhere in the airway, or they don't hang around. They aren't going to sit there and later be passed on to someone else.
I can understand other sorts of objections to this line of thinking, such as virus numbers being to low to be able to transmit the disease from the nose, throat, and lungs of immune persons to other persons, but I do not understand your argument. I thought that hanging around is exactly what viruses do until they are destroyed. If the airways of an immune person is not actively destroying the virus, I would have thought that the damp interior of a human body is a fine place to hang around, rather than on surfaces on door handles and so on, where the virus can be desiccated.