I was thinking the same thing; still, if the gigafactory is able to get battery costs way, way down, the concept possibly could work. Part of the goal of the gigafactory is to produce battery packs that can shift power demand, i.e., charge the pack when electricity is cheap and then draw from it during peak demand hours, thus smoothing out demand & lowering costs. The same pack could be the heart of a home supercharger.
The size of the pack needed for a supercharger would be determined by how much you expect to have to charge the car. For example, to keep costs down, you could design it so that the supercharger pack could bring the car up (at most) from 20% charge to 85% charge. Then the battery would not have to be bigger than the battery in the car; it would just need to be wired in such a way that the voltage of the pack in the supercharger is higher than the voltage in the car (this works even if the supercharger has a lower kwh than the pack in the car, because charging is driven by voltage, not capacity).
To your other point, though, yes it would still be expensive. But it could also be set up for solar charging; that feels like the future to me.
