Here's an approximation of what is happening:
The blade slows down a slug of air (mostly on the upwind side of the blade, although its influence also slows some on the downwind side - especially if it's a good airfoil shape). The wider the blade, the longer the slug of air it slows down.
The gap between blades lets the slowed-down slug of air go through the mill before the next blade's influence arrives at that position.
If you have the blades sized so the next blade's influence just arrives as the last of the slowed-down slug of air gets clear, you're collecting about all the power you can from the cross-section of the wind that goes through your blades.
To do this, the fewer the blades the wider each blade has to be (although a good airfoil shape lengtens the slug of slowed air and thus acts like the blade is wider).
If you have blades that are too narrow for the number of blades, some of the unslowed air gets through the gap before the next blade (or its leading influence) arrives. So some air gets through without being slowed down. Adding more blades improves your power output, up to the point where you're slowing all the air. After that, adding more blades gets you no more power - because part of the air each blade catches is already slowed down.
More blades lets you get higer torque and lower speed. This is great for a patent windmill with a reciprocating pump, because you want to lift a bunch of weight. But it's mainly done because patent windmills were designed by guess and by gosh and by cut and try, before aerodynamics was well developed. (Also because sheet metal is cheap.)
But for generation you want high speed. The faster your magnets move, the more power you get from a given amount of magnet. This means a faster shaft lets you buy fewer permanent magnets (or burn less excitation power for electromagnets) to get a given amount of output power.
Therefore a wind generator will tend to have either few broad blades or a bunch of narrow ones. If you're home-brewing it typically costs you more effort to do a bunch of blades than to do a few wider ones, and a low-count turbine is about as efficient as a high-count. So there's little point in going to high blade count (unless you have an easy way to make a lot of narrow blades that are individually not very strong, which doesn't scale up to making a few, broad, strong blades).
Two blades have a problem with vibration on yaw, so you want at least three. Typically you'll see three or five carved airfoil blades, or a bunch of some inexpensive and easy-to-fab curved-sheet approximation (like your cut-barrel blades).
