You end up with an incredible amount of mass divided by 4 or 5, which most likely works out to an incredible amount of mass.

In one of the patents, they work out an example system that can handle 30 megawatts, which might be the output of 10 or 15 turbines. The system absorbing the 30 megawatts for 30 minutes has a working mass of 1200 tons (conveniently, they use a working height of ~600 meters).

So all you need is a system capable of lifting 100 tons a distance of 600 meters (to store 1/2 hour of output). Which is probably something we are capable of building (there are cranes that lift much more significant distances), but it probably isn't something that would be economical.