In the case of applying higher voltages if the channel is made of a conductor, there must be a very good insulator on the channel surface (usually glass or plastics). Why?
In electrophoresis current flows from the anode (-) to the cathode (+), that is, anions made of SDS surrounding proteins flow towards the cathode (+), just like in the old TVs (electrons illuminate in Cathode Ray tube, the tube).
So there's a net flow of electrically charged molecules from one extreme to the next, without any other source of electricity. Many electrophoresis chambers have wiring in areas that might disrupt the architecture of such electrical flow and that's why they should be covered with insulator to avoid disruption in case voltage increases significantly. Plastic is common, I haven't seen glass but it's a good insulator. Of course, insulator should not cover the cathode or the anode.