> recall most of them operate as giant annual batteries, they refill in the rainy season once per year, then dispense that energy over the dry season
That’s not quite how it works.
Consider the biggest hydro project in US, the Columbia river, with its 14 dams.
The system does fill up in the rainy season, but the crucial thing is that it’s not the dams that do fill up, but rather the whole watershed, meaning things like snowfall and ground water. This means that we have very limited amount of control over when we let the water through. We can’t just dam the river for an extended period: if we don’t use it for generating power, we must spill (waste) it. This means in practice that the dams are not batteries: to a large degree, it‘s use-it-or-lose-it.
To make these into batteries, we’d need to somehow refurbish the dams to tremendously increase the power generating capacity on each dam, so that instead of assumption of continuous flow (either through turbines or spillways), we make the flow more intermittent, so that we can make up for closed times by pushing more water through during open times.
This is tremendously difficult in practice: dams are simply not designed to allow for refurbishing with many more turbines or much more flow through them than they were originally designed for, the upstream reservoirs are not designed for quickly varying water levels, etc.
Point is, we can’t just “save the water”.