Because we are very good at building turbines.
There are alternative methods, like photovoltaic like solar panels. We can use heat directly to make electricity. We can chemically make electricity. The problem is that these methods are all inefficient in some way or another. With a turbine, we understand the effect pretty well: Spin some magnets around a wire, and it will generate electricity via induction. Most methods end up being a turbine because it would be really difficult otherwise. Converting heat directly to electricity without a turbine is incredibly inefficient, less than 10% of the heat is being turned into electricity. Modern steam turbines can reach as high as 80% efficiency. With rates that high, it becomes difficult to suggest using anything else. Nuclear power plants, coal/gas plants, hydroelectric, wind, geothermal and wave turbines all follow this principle. There just different ways to spin those magnets.
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