Speed is what we are looking at to generate power.
Actually, horsepower is what you are looking for to generate power - RPM times torque.
It's convenient to have high speed at the gap of the genny - the higher the speed there the more power you can get from a given set of magnets. But building a genny - or a genny plus transmission - that is matched to the torque and RPM of your turbine is a separate issue from designing the turbine to collect power.
If you increase the diameter just for swept area sake most of the wind just blows through and the turbine runs too slow in common winds and puts more stress on the upwind blade.
You'd think that, but it's wrong.
The key is that the blades are MOVING. They affect (and draw power from) the air for a significant distance upwind and downwind of themselves, not just the tiny bit of air that actually touches them. So when they move across ("sweep") an area, they draw power from a slug of wind the crosswind width of the area (plus a tad) and for a significant up/downwind depth. While they're out of the way the slowed slug blows downwind and another comes in from upwind. Then another blade comes by and pulls power from THAT slug.
Design your blades that they come around just as, or just before, the old slug clears the active zone and you get to pull power from all the air that passes through the swept area. As the wind speeds up the blades speed up in proportion so the geometry of the blades and slugs remains the same.
Similarly, scale up both the radius and the blade width and you continue to sweep power from the scaled-up cross section. The speed goes down, but the torque goes up to more than compensate. Double your radius while retaining the same height and you cut your speed in half and multiply your torque by four. (One factor of two on the torque comes from doubling the lever arm, the other from doubling the width of the blades. Scale up by 2 in all three dimensions and your speed still goes down by x2 but now your torque goes up by x8.
That's why, though a turbine may only block light through a tiny amount of the cross-section, it pulls power from all of it. (It also is why, when it's spinning under load, it has drag like it was nearly a solid barrier across the whole cross-section.)