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It's not worth it. The energy you would generate is proportional to the vertical drop and the mass of water. If it were a river's worth of water then you could generate a significant amount of power, but there just isn't that much water mass in the steam.
You can use the leftover low-pressure steam for other purposes. For example, some places have combined heat and power (CHP) plants that use the steam to heat buildings, or run industrial operations that need a lot of heat energy. Though that requires you to live or work next to a power plant, which many people don't like.
Yup. By the time it's released, most of the energy has already been extracted from the steam. In the boiler, it was high temp and high pressure, then once it's gone through the turbine(s) it's cooler and low pressure, not really energetic enough to turn another turbine.
I'm talking about capturing the vapor, letting it condense, and then dropping the condensed water from its capture point. It's not about exploiting the remaining energy from heat & pressure contained in the steam, but exploiting the gravitational potential energy created from all that water vapor rising and coming out the top of the cooling towers. Kinda like how we create energy batteries by pumping water uphill into a reservoir for later use, except we wouldn't have to use any additional energy to pump it uphill.
So you want rainpower, but worse? Water batteries are a thing, but the amount of water in that vapor is miniscule compared to the amount required to generate enough energy to make that kind of infrastructure even remotely worth it.