I set the front course of the localizer on the CDI instrument anyway, even though the representation on the instrument remains the same whichever course you set. One of the advantages of this is that you can easier see the WCA (wind correction angle) during approach, since one would set heading bug to the actual heading that keeps the aircraft on the localizer - since this is the heading you will have to maintain in order to fly towards the localizer in case of missed approach (unless a procedures dictates immediate turn at MAPt). Peter also mentioned that some autopilots require the correct course to be set in order to fly the ILS accurately - Piper Autocontrol is one of them.
But the real advantage is that, if you have the luxury of standby frequency on the NAV receiver, you can preset the VOR if the runway has a VOR approach. In this case, if localizer goes offline, it only takes one push, turning the approach plate around for the new minima and off you go on the VOR approach (provided you're not very close to the runway). However, I usually have the VOR for the VOR approach tuned and set on the 2nd CDI so I can cross-check during the approach. And
nothing happens so fast in an IFR flight you wouldn't have time to change the VOR frequency and set the appropriate radial - unless you're flying single-pilot jet I suppose
