I think you are wrong here. Consider a windmill as a sail on a ship. The ship gets pushed in the direction of the wind. Without a windmill, the wind would just blow over the land. But with the windmill, the wind 'pushes' the windmill. So, the windmills will cause the earth's rotation to speed up. Days will become shorter. We may spin out of orbit.
Actually the wind turbines do take energy out of the wind but the energy will be restored downwind due to heating from the sun.
I do think there may be a problem of creating a rain shadow for a ways downwind if there are enough windmills but I don’t think any serious studies have been done. Seems like there were some stories about warmer ground level temperatures under windmills at night in Texas. I think it was due to the turbines not allowing an inversion layer to form.