Rain Power?

The other day in the shower I was thinking about how most of our forms of energy are essentially either solar radiation (possibly assisted by gravity), tectonic forces, or stored results of these processes.

Solar energy comes from solar radiation, of course
Wind energy comes from solar radiation, causing motion of air (and helped by past tectonic activity to focus the flow)
Hydroelectric power comes from solar radiation evaporating water, wind depositing it elsewhere, and gravity pulling it towards a generating station (with past tectonic activity providing a narrow channel)
Geothermal energy comes from tectonic processes, bringing energy up from Earth's hot interior
Biofuels like ethanol and wood come from solar radiation helping plants grow
Coal comes from plants that grew thanks to solar radiation, then got concentrated thanks to tectonic forces
Petroleum comes from plants that grew thanks to solar radiation, then got concentrated thanks to different tectonic forces
Natural gas comes from plants that grew thanks to solar radiation, then got concentrated thanks to more different tectonic forces (consummate forces!)
Tidal power is an outlier, depending entirely on gravity (and, I suppose, tectonic forces from long ago)
Nuclear power doesn't fit this model, and derives from the atomic strong force

So, I thought to myself, could you harness the power of solar radiation plus gravity by intercepting falling rain or snow? Like a turbine that gets turned by sufficient raindrops? Or a fulcrum which raises one side when the other side gets covered in snow, creating potential energy which can be converted?

I was thinking this could be deployed in places that get a lot of rain like Mount Wai‘ale‘ale, Mawsynram, or López de Micay or a lot of heavy snow like Sapporo or Syracuse.

I wonder if the problem with this idea is the wide coverage area needed to get a reasonable amount of power. A hydroelectric dam gets to use time-delayed rain from a whole region, but misses out on the cloud-to-ground potential energy.