If you're going mechanical, why not pumped water storage instead? Nothing has to spin super fast and hydro has a lot of maturity.

(From a guy who got burned buying stock in a centrifugal system as my first "wicked smaht" investment as a 22yo).

there are areas where almost all options for pumped hydro are already developed and there's little room for expansion. additionally, the heat waves from the climate catastrophe affects pumped hydro negatively (evaporation and higher water temperature).

Mostly because we already used all suitable places. It also has a huge environmental impact, large upfront costs that you can only spend in bulk, permissions, lawsuits, protests from the local population and so forth.

Hydro is limited by geography. It cannot scale in the same way. Rather than giant spinning masses at central locations, current thinking is more about smaller masses scattered throughout a grid. There are even a few studies on whether existing air conditioner/heat pump compressors could contribute.