Why not four or five or even more?
Intuitively, the more leaves the more power.
So, what is the reason?
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I worked at the Wind Energy Project Group at the TU Delft in the Netherlands for a summer. One of the most interesting ideas was a wind turbine which only had one blade, with a massive ugly blob on the other side as a counterweight. The idea was, "if we spend three times as much money manufacturing just one really good blade, could we make the system better than if we spend the third of the money on each of the three blades?"
If you understand this, then you understand what's really happening. In general the power plant is not optimizing for power. It's trying to maximize energy while minimizing cost and part failures, so as to maximize some "value" that the wind turbine has overall. Put more blades on to get more power and you might need an even better turbine inside to convert that extra power to electricity: and this might be more likely to fail at the higher RPMs you're using. The designs which maximize this may involve having 5 cheaper, smaller blades, or 3 more expensive, larger fins. The expense you pay may be in how strong the blades themselves are, or in how perfect their curvature is, or how long they are (raw materials)... but it will be a complicated function which determines how few blades are optimal.
It's the same reason that most airplane propellers have only two or three blades. As the blade moves through the air (or the air moves over the blade), it leaves a wake. If the next blade encounters the wake, it will be moving through disturbed air and will be less efficient. The more blades you have, the more likely each blade will pass through air disturbed by the one ahead of it.
Faster aircraft tend to use propellers with more blades because they need the extra thrust provided, and the added speed tends to keep the wake clear of the propeller disc, so the blades are always meeting undisturbed air. Since a wind turbine is dealing with relatively slowly moving air, the turbine could rotate through a significant angle before the disturbed air moves out of the turbine disc; more vanes means more likelihood each will operate in the disturbed air coming off the preceding vane.
For what it's worth, just as there are single vane wind turbines, there are also single-bladed propellers. You don't see single-bladed propellers very often; but they have shown up on model gliders (miniatures) where every last bit of efficiency matters.