I have read that due to the skin effect we only need to coat e.g. cables with a good conductor to make them effective. I understand that when a em wave is incident on a conductor it only propagates so far into the conductor dictated by the skin depth. This happens however, when the em wave is incident onto the conductor from another medium, not like in the case of a cable where it is travelling along the conductor itself, i.e. they are not incident on its surface but travel parallel to the surface. How does the skin effect relate to this latter situation and why does this mean that we only need to coat a cable with a good conductor.
Coating a cable is done for two reasons. Firstly any external noise doesn't go into the system and secondly, to not let the signal go outside. So due to the first reason, coating with a good conductor is essential as any external signal will be go only upto the skin depth. As for the point you raised about the parallel transmission of signal, then if the signal goes parallel to the cable, there is no need for coating at all as by definition it won't stray from its path. However practical cables don't remain parallel at all times and so at some point of time signal will be incident on the cable. Then the description as you mentioned will follow.