Not always:  The purpose is to extract work form the wind.  You do that by diverting it, of course.  But you can sometimes extract even more work from it by adjusting its speed.  That's what a wing does - forcing the air to take a longer path, flow faster, lower its pressure further, and thus generate more lift, on the topside of the single foil.

And that's why lift-type mills, both vertical (darrieus) and horizontal (the ones that look like propellors, rather than the drag-type that look more like fans or blowers) have thick blades.

I like your double-bladed design as shown above.  (I'll delve into your web site later.)  Between the picture and your description it sounds like you're doing two things that sailboaters have done for a while, but applying them to a mill to good effect:

First, you're using a doubled blade - like the jib and mainsail on a sloop, the simplest of the multi-sail designs.  The jib does two things:  It provides its own lift, of course.  But it also directs the wind against the backside of the mainsail.  This improves both the attachment and the airspeed on the lee-side airflow of the main, increasing the power of the main.  You get, more power, power going TOWARD the wind (though not straight into it) and with two sails you get power at a TIGHTER ANGLE toward the wind.  You also get a more forgiving adjustment on the sail angles, which, in a rigid blade configuration, amounts to getting good power for a wider arc of the rotation.  An important point, though, is that the extra blade gives you the ability to increase the speed of the air over the leaward side of the (trailing) blade using only thin blades, rather than requiring a thick structure.  So you get a lift-type turbine with thin blades.  (You might think of it as separating and reversing the top and bottom sides of a thick blade, though that's probably distracting from what's really going on.  B-)  )  It also means you can have a TSR greater than 1 and optimize your leading and trailing edges separately.

The experience gained with the device I have over the last 12 months it has been running is that (1) the doubled blades allow it to start up and run (no small feat!) instead of sitting there without flow attachment on the blades and refusing to do a thing in the wind and (2) making the doubled blades thinner allows it to run faster instead of just turning as slow as molasses. This has been a total revelation to me and I'll bet my excitement shows.

And diservedly.  The combo of the blades makes it act like a drag turbine at startup, then switch to a lift turbine as it speeds up.  Good work!  (Like a Darrieus with a Savonius starter rotor, but without the non-optimized Savonius in the way when you're up and running.)

Second:  Sails themselves are thin but (except for jibs) the mast provides a fat leading edge.  Your text sounds like you've done something similar.  (I'll dig into your web site to see if this is a correct reading.)

The other thing is that I am sure something can be learned in the case of the horizontals from this as well.

Perhaps.

But lift-type horizontals are already well-developed and pushing the wall on efficiency.  The Betz limit tells you the maximum power can be extracted from a given airflow, and they're within a couple percent of it, so there's not a lot of room for improvement.