At some point the amount of copper needed to carry the current becomes heavier than the batteries themselves. 120kW is already outlandishly strong, at 120V it's 1000 amps!
If you had batteries which could accept that (Li-Ion's don't like going above 3C I think) and had the kind of energy density being claimed then it would be a relatively trivial matter to use a larger bank of them to provide the peak capability to charge a smaller bank of them.