The mop can also be used to apply copper solvent although a nylon or bristle brush is often used for that. If you use a bronze or brass brush to apply stuff like Sweets 7.62 or Hoppes 009 copper solvent it will aslo disolve the bronze or brass bristles as well.
I must admit that I never use the mop. I don't leave oil in the bores and I keep spare bronze brushes in and do use them to apply any solvents used in cleaning. If they wear out they wear out and are replaced as they are not that expensive and by doing so they do remove any nitro fouling and so allow the solvent to get to work on the fouling underneath the glazing of the surface.