Consider the application. You have to get the two hots and ground to the [remote] switch, which breaks both hots, if 240, or the hot and neutral, if 120. Then you have to return it to the motor. As such, you either need two cables, or one with five conductors.
The collector [currently] operating off 120 could have been altered with a single conductor, just as you would a household light, but a second would have to be added when the collector was switched for 240 operation. Might as well do it now, while everything was open, rather than reinvent the wheel later.