My understanding is that peak power availability is at least as important as total energy storage. (The main use of grid storage is to handle spikes in usage,

My understanding is that peak power availability is at least as important as total energy storage. (The main use of grid storage is to handle spikes in usage, or similarly to fill in for dips in generation - like from wind turbines. Either way, peak power available is important.) One big weight would give you significantly more peak power than several smaller ones. Yes it would require more or stronger cables, motors, and other infrastructure, but the cost of all those is small compared to the shaft, so I imagine a single weight would maximize peak power / cost.