I hesitate to get involved in this argument as the positions are so entrenched. However, a little observational input may assist.
I was working as local/tower controller at Valley in Anglesey. It was a quiet Sunday and as was quite common there the wind was gale force although steady and not gusting as it came off the Irish Sea. The surface wind was almost due West and probably 50Kts at least (it was a mbmmble time ago).
A Stampe biplane wished to depart back to England to the East and 'taxied' if that is the right word for driving straight into wind onto the grass at close to full throttle with members of the visiting aircraft flight on both wings and fuselage near the tail plane. The pilot asked for takeoff and waved off the VAF crew and the tail of the Stampe lifted up and then the aircraft effectively took off close to vertically into wind. The aircraft climbed to around 200 ft straight up, then turned left steeply cross wind then downwind onto East. As it did so it lost a significant amount of height as it also gained a significant amount of speed. The last call to me in the tower from the pilot was: "I won't be coming back!".
Yes I know all the arguments about being in a windfield so the ground speed doesn't matter - but I had the feeling that it did. The inertia of the aircraft that was close to stationary had to be overcome for the aircraft to depart at (guess) wind of 60 kts at 200ft plus aircraft eventual flying speed of say 60kts meant that the airframe had to accelerate from stationary to 120kts - agreed helped by the airmass it was in. That inertia has to be overcome regardless and that is due to the frame of reference to the Earth/ ground speed of the airframe. So an extreme example but I assure you that the aircraft lost a lot of height in the turn going past at my eye level in the tower. A more gentle turn may have masked the effect but it would still have been there.
I think it is a case of relative speeds: wind speed to aircraft speed. A military fighter at 400 kts + in a relatively low wind may not notice the effect. An albatross at 20kts may notice the inertial effect of a turn in a wind of equal velocity.