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.

Short answer you are correct it's not worth it. The massive cost of a bigger tower and gravity turbine aren't worth the tiny energy you get.

This video covers the basics of how cooling towers work to reuse as much of the energy as is reasonable.

https://youtube.com/watch?v=tmbZVmXyOXM

The energy generated by such a construction would be proportional to the mass of water that falls (as is basically every other form of energy generation), which is a problem because the m here is way too small to be worth it. The steam looks like a lot because you're going by volume, but gases in general are just really light. To get an idea of how light, steam at 125C will shrink to 1/1800 of its volume when it's condensed into water. In other words, a 1-meter cube of steam would become an 8cm cube of water. You can find this out by plugging the numbers into the ideal gas law, but either way there's just not enough steam up there to be worth it.

I'd guess because it does not produce enough power to justify the cost of creating the condenser/turbine, otherwise, they probably would have.

Even assuming you had 100% efficient, and totally free energy capture systems for the evaporative clouds you see coming off the cooling towers... You probably wouldn't use them because of the need of the primary system for time based cooling.

Any capture and recycling system will slow down the cooling rate of the primary system, if your goal is to use the primary system to maximum efficiency then that cooling rate can not be slowed down. .

How would you cool the water to condense it?

Getting it to cool efficiently is actually a very interesting challenge. Certainly more challenging that I thought before watching this https://youtu.be/tmbZVmXyOXM

Because efficiency. The amount of power generated from the water fall would be minuscule compared to the power generated from the stream.

Any engineering effort going into making this process more efficient would be better off making the steam generation more effective.

Short answer is because it isn’t worth the effort.