The "1" is the system name because the sensor is basically a 1 inch type sensor{1 inch video sensor is 12.8mm x 9.6mm and the CX is 13.2mm x 8.8mm}. The old video sensors were tubes and were measured by diameter. When sensors became flat they kept the old size names even though the actual sensor is smaller than the name implies. The same goes for 1/3, 1/2, 1/4, 2/3 and even the 4/3 sensors. So the system name is "Nikon 1" and the body name is J1 or V1 and coming soon J2 and V2.
A sensor double the size would be very nice, about the same size as the Canon APS-H. However the APS-C is only a tiny bit smaller so I can't see Nikon using both. However a system that is mirrorless and styled similar to the 1 and using an APS-C sensor is possible. I know I would get one especially if it could easily mount F lenses with full controls{can live without D focus drive and pre-electronic control}{but should be able to use every old lens in manual and maybe aperture priority modes}. This would also be a good marketing move by Nikon to combat the new Canon EOS-M. Perhaps they will? Nikon 2? Nikon-M? I would buy one, that I can promise you.