With seven orders of magnitude of difference, you'd have to dig a whole lotta holes before hydro has to start worrying about competition on the capacity level.
Many of these projects also falsely assume that there are enough abandoned mineshafts or other types of holes to convert into a battery storage system. They have to do this because you would see through the scam immediately. Digging a wide and deep hole is expensive and not economic unless there is something valuable at the bottom of the hole.
There is also the fact that weights are expensive relative to the energy they can store so you have to take them directly from nature (usually via dams or pumping water uphill).
Right, the thing to worry about is power, not energy. Ideally the pumps would be sized to fill/drain lake Powell in 12 hours. Which is ludicrous. The turbines in the Glenn Canyon Dam have a max (output) capacity of 890m^3/s [0]. It would take just over a year to drain the reservoir through them.
Which is fine, as many regions have a strong seasonal availability of renewables. Storing energy for some months will be required to go fully renewable. There are also short term storage requirements, over the course of a day or a week.
Compared to energy loss over distance, which you don't really have if you dig your hole right next to you, it's more like 6 orders of magnitude, maybe less.
But maybe capacity is only part of the story. What about locality? Distributed energy storage may not be as efficient, but it has a lot of other benefits.
