If charges flow along the surface of a conductor, why is resistance a function of cross-sectional area?
The skin effect is an effect of frequency.

At DC there is no skin effect so the resistance is a function of the cross section of the conductor.

As frequency rises, the current tends to decrease at the center of the conductor as you said. For the current to flow only at the surface of the conductor, the frequency of the current should be infinite. In reality there is always current flow with diverse density at different depths of the conductor, but there is never current "only on the surface".