The physical battery idea has been a thing for decades in the form of a pump storage plant where during times of excess electricity, they pump water up a hill, and when power is needed it works like a hydroelectric power plant. The problems with these however is that in order to get a meaningful amount of power and longevity, you need a lot of water and space to build one of these which makes them massive and expensive up front. I have one near me, but I also live near one of the biggest lakes in the world, which helps.
Yes, pumped storage is definitely an existing technology that serves this need. I live near a massive one as well. However, large-hydro recently has not been considered as renewable form of generation due to the disruptive impact it has to local ecosystems.
I know in the US, new projects do not get approved due to permitting and water board issues. So I don’t think we’re going to see any new construction.