We can’t really expand on hydroelectric dams; we already have dams in just about all locations where they make sense. If there’s no convenient hydro dam near you you’re probably going to have to go with something else for storage.
Also, those dams are usually used for power generation; for storage it’s more common to use pumped hydro where you store energy by pumping water to a higher reservoir and release it by letting it flow to a lower one. A major downside is that pumped hydro only works in select locations; not every hill is suitable for installing a pair of large cisterns.
Another option is compressed air energy storage, which stores energy by compressing lots of air in large tanks and then releases it by letting the air back out. Cleverly designed implementations can even make use of the thermal changes the air undergoes at its density changes. They also need specific local conditions; huge high pressure tanks are hard to build so we usually use things like salt caverns as tanks. One interesting option is to use depleted natural gas fields.
There’s also other options like flywheels, which should be a bit less picky about location.
And lastly, not every battery needs lots of rare earth metals. Sodium batteries are currently starting to hit the market; they are more stable and less reliant on rare materials than lithium batteries. They are also bulkier but that’s not much of a concern for a grid-level storage facility.



Why? Plenty of dams are perfectly capable of producing power 24/7. It may not even be possible to let the reservoir fill up during the day and drain it during the night, especially during a drought or flood period where the amount of incoming water very much dictates what you do with your dam and when.
You make a lot of assumptions about how dams are operated. Those assumptions aren’t always true.