I learned about a new law today. Betz’s Law.
Betz was a guy who decided to calculate exactly how much energy could be extracted from the wind by a turbine at any given time mathematically (as you do).
He worked out that no turbine can take any more than 59.3% of the energy from the wind. To be able to conceptualise this, you have to think about wind like a physicist.
The first law of thermodynamics states that you can’t create or destroy energy, you can only convert it to different forms. Therefore, all wind is just energy in a certain form, and in any system there is a point where the transformation is most efficient and beyond there it takes a lot of effort to get any more energy from the system.