In horizontal axis wind turbines, why does axial component of absolute velocity stay constant (wake rotation theory)

The windmills based on lift action don't change the speed of air passing through them same as an airplane's wing flying through the air, the air stream washing around the wing's top and bottom doesn't pick up any speed. It Just gets bent down.

The blades of the windmill in this case work like a wing they let the air stream through but they bend it by twisting it as a screw driver, albeit that twisting will calm down rather fast by the viscosity of the air.

A crude example of the flux of the air before and after the windmill would be like those striped colored toothpaste, going straight till it hits the blades then twists a quarter of circle then keeps roping out straight behind not turning anymore, and getting mixed with the rest of the wind. this is kind of cleaned up version of the affair, other wise there is some turbulence and a bit of drag, etc.

So the axial speed of the air remains the same but the tangential speed changes for the transit time starting from the encountering the tip of the blade till some time after leaving the trailing edge of the blade.