Transmission Line Model for Coax wire
The resistance of the outer and inner conductors are important – but just not in the way I think you think they are.

The resistive element in the equivalent circuit doesn't exist because the energy has to flow in the conductors from start of the coax line to the end.

In a a waveguide such as a coax cable, energy is transported as wave within the dielectric – and losses within that isolatig material are usually at least as important as the losses of the edge currents in the surrounding conductor.

When you start looking at the depth of how much the wave on the inside of the coax cable permeates into the center conductor, you'll find it's often a couple µm only – and hence, you can find a lot high-quality cables where that conductor is actually made of steel or aluminum, and is only coated in a thin layer of copper.

The same applies to the outer conductor. Due to geometry, the field strengths are typically significantly smaller than at the center conductor, and hence, losses in the conductor don't contribute to overall loss as much; that's why it's common to find thin foils as outer conductors of coax.