The result as 16/27 can favor drag power systems (Makani, FlygenKite…), horizontal-axis turbines (HAWT), and generally rotating devices like Rod’s Daisy or Rotating Reel or autogyro-like (https://www.youtube.com/watch?v=gExAQq2VzgQ). All these devices have a stationary rotor and convert wind power by using torque, while lift power devices (yoyo) use traction.
Let us try to check this with an example, wind speed = 10 m/s, air density = 1.2.
The power of a HAWT is determined by the disk swept by the rotor. Supposing the disk area is 100 m².
Power at Betz limit: 1/2 x 100 x 1.2 x 1000 x 16/27 = 35555 W.
Now let us take a surface of 100 m². Traction (force): 1/2 x 100 x 1.2 x 100 = 6000 N. Let us reel-out this surface in the optimal speed of 1/3 wind speed, considering the wind speed on the surface is now only 2/3 wind speed, leading to the result: 20000 x 4/9 = 8888 W, so exactly 1/4 of 35555 W.
Checked!