Efficiency (and therefore power capability in a given environment) of a wind turbine is largely independent of blade count*, assuming an optimal design. All that is required to extract maximum power is that you need to interact with all the air passing through the rotor disk. With fewer blades, this is achieved by spinning the turbine faster relative to the incoming wind, so all air still passes within a relatively close distance of a blade and interacts with it. Modern wind turbines use a 3 blade design for a few different reasons.
One major factor is that 2 bladed turbines are prone to a fairly large oscillation in loads at the hub and nacelle during operation. This happens because there is nearly always a wind shear near the ground, so when the blades are vertical, there is a large torque caused by the top blade encountering higher wind speed than the bottom blade, and therefore having a much higher thrust load. However, when the blades are horizontal, this load doesn't exist. Because of this, twice per rotation, this torque is applied and then released to the nacelle. A 3 bladed turbine is always subject to the wind shear, so it tends to have more of a static load rather than these large oscillations. There are methods to mitigate this (you can research teeter connections if you're interested), but this is a problem that 3 blades solve.
Also, noise is strongly dependent on blade tip speed, and a lot of modern wind turbines are noise constrained by regulations. 3 blades enables a significantly lower tip speed (33% lower) than 2 blades for the same power extraction, reducing noise emissions from the turbine. Adding more blades would of course continue this, but you do start to get diminishing returns
One benefit you do get by going to more blades and higher solidity (proportion of the rotor area obscured by blades) is a large increase in static or low RPM torque. This is why the classic American "windmill" you see all across the great plains for pumping water in the US has so many blades - it enables it to start easily, even in low wind, and have plenty of torque to start with the load attached (so no complex clutching mechanism is needed). Similarly, the 4 blades and high solidity of the Dutch and northern European windmills would do similar - they would have plenty of torque at low RPM, which would probably be beneficial for milling, and maximum power and efficiency was probably not a concern. However, for power generation, you want relatively few, slender, high speed blades, as you can control the generator torque to ensure that the turbine is able to start, and you want to maximize power output and minimize cost and materials.
*For the truly nitpicky, there is a slight blade count dependence, and you lose a couple percent efficiency with 2 blades compared to 3, but this is pretty minor, and nobody would decide on blade count for this reason alone.