Here's an example of why you might want to run only 3 wires: in constructing a long extension cord from flexible stranded copper wire, you find that 10-3 wire is readily available but 10-4 is not nearly as common. So I constructed my long cord to operate only at 220 with 3 wires. If I need 110 at the far end, I use a cheap voltage converter transformer, where the secondary of the transformer is center-tapped. The center tap re-creates the neutral circuit for 110 use. And by running only 220 on the extension cord, you get only half the voltage drop (for a given load) that you would get by using a 110 cord.
