Fatigue and fatigue related impact on overall efficiency might be the biggest concern about this - next to the amount of CO2 produced just for the concrete and the unused energy in start and stop of the motion... No doubt that there could be a working prototype, but this is really about longevity and which efficiency is acceptable for a storage concept; i would not operate this in an area with earthquakes or high wind.
It would not even need to be a freestanding tower, something similar could be installed in closed mines under ground, which do have longer slopes or elevator shafts. It might not be as many and rather small, but longer distances and higher weight would be possible, as there is a support structure enabling some safety features in case of a failure. The longer distance would offset the problem with losing to much potential energy through stacking next to a very limited height of a freestanding tower.
There are other similar concepts, like lifting weights with water pressure to store energy using conventional pumps and turbines. The weight could be locked in place and it would mean less moving (wear)parts, plus the benefits of a mass with higher density than water in the system and a lower loss by hydraulic control. This could shrink the required volume for a pumped storage hydroelectric plant by the difference in density of all media used and enable to use it in places otherwise not suitable.
However, since a few years Power2Gas is the concept that gains a lot of traction here, it uses the natural gas network as storage, small and big installations are in the making and working. Given that gas turbine generators allow a fast start of electricity production and are all over the place to cover shortages, this makes more sense. Not saying it is that easy, because hydrogen penetrates some materials and combustion processes are never fully ideal.