Actually filters need to be washed for two reasons that have nothing to do with removing stuff from the surface.

The first is to make sure that the filter adheres to the funnel and the whole system is warmed to the correct temperature; the second is that (especially with V60 which always seemed to me like a proper chemistry experiment) you have to soak the filter so that none of your carefully weighed water is "wasted" in the filter but goes to extract the coffee from the powder.

In a chemistry lab wetting the filters prior to use is common practice, more so when a vacuum system is used in order to have a good seal.