If you wanted to recharge an electric-drive car's battery pack in 1h, you would need an electrical circuit rated for 400A/240V and a battery able to absorb that much energy that fast. Easier said than done and some people may have trouble handling cables that thick.
The dry joint issue can be mostly solved by simply adding an air bladder at the top to compress the balls after they have been loaded so cells won't shift or break contact so easily.
I agree that energy density, both by volume and mass, would be questionable at best - stacked lithium cells are already at the limits of being practical without the extra weight and volume of fully enclosing individual cells, along with the routing MOSFETs' losses.
As for some cells not getting used, that is not necessarily a significant issue as long as you only get billed for the difference between the charge in the cells you dumped and the cells you picked up.
Sounds like a EV solution with changeable batteries made from small modules. I have doubts about tank construction and bigger capacity claims, but it may work. I have not seen real thing besides the site, it would be interesting to see it action.
It would be much simpler to simply come up with standard EV battery pack sizes, capacities and locations so they can be quickly swapped out when fast-charging is either not possible or still not fast enough. If swappable batteries become part of the energy delivery infrastructure rather than individual property, battery packs would get progressively upgraded over time to deliver more billable capacity at lower labor and material costs.