Reddit mentions of Wind Energy Handbook

Their second slide states their design has a greater cross surface area. This is not how it works. The reason area matters is because of this equation:

Power = (1/2) x (air density) x (area) x (power coefficient) x (wind velocity)^3

The area in that equation is dependent on the length of the blades. Not on how much of the circle is covered by blades. So if you have a design with a 50 m long blade, the cross sectional area will be the same regardless of whether your turbine design uses one blade or 15 blades. What changes is the power coefficient.

What they should say is that their design has a higher solidity.

There's a fair bit of aerodynamics at play here. But the maths shows that optimial efficiency (the power coefficient in the above equation) is achieved with three blades. As you increase the number of blades (thereby increasing the solidity) beyond three blades, the maximum power coefficient drops.

With that said, these types of turbines do already exist, mostly in the form of wind pumps. They are designed to work in low winds, with lower RPMs but where high torque is required (to pump water). For those uses, a design with high solidity works. But for use in high wind scenarios where the purpose is to turn a generator, the three blade design works best.

The other problem with more blades is that you are increasing the costs dramatically. The utility scale turbines discussed in the OP are very tall turbines with long blades. The additional costs involved in increasing the number of blades would be very high. Firstly the extra blades would cost money, then the hub design would be more complex, and the hub and nacelle must be stronger/heavier to support the extra blades, this means the tower must be stronger/heavier to support the extra blades and heavier nacelle and hub, and finally, this results in the requirement for stronger foundations. And all this extra equipment also means higher transportation costs.

Also, in the slides, they state that the three blade designs are fixed in their position and can't turn to face the wind. This is simply not true. All utility scale turbines can and do rotate to face the wind direction. It may be the case that small scale turbines do not turn into the wind, but I'm not familiar with turbines of that scale.

So though it's possible that high blade count turbines have applications at which they excel (wind pumps, possibly with small scale generators), utility scale electricity generation is not one of them.

Source: Wind Energy Handbook