An example of the reason which I don't accept the "parcel of air" concept to the exclusion of an inertial factor is as follows:
If, in my STOL modified C 150, with it's original 100 HP engine (so low power), I take off directly into a 25 MPH wind (north, let's say), I can be airborne, and initiating a turn at 50 MPH IAS. That will be 25 MPH groundspeed (GS). Yes, I know that the 'plane does not know its groundspeed, but the 'plane still is subject to the inertial forces of rigidity in space (or something like that, I'm not a physicist).
Now I'm turning away from north, with 50 MIAS, and 25 MGS. I will soon be flying west at 50 MIAS, and a changing GS. But, somewhere along that turn, before west, my GS along the north/south line will be zero. Then, moments later, I'll be flying south, 50 MIAS, and what will the GS be? The math says 75 MGS. For the purpose of this discussion, subject to expert physicist comment, GS is relative to rigidity in space for the 'plane, irrespective of the parcel of air. The 'plane still has inertia.
So, my question: Can we expect the lowly 100 HP C150, in a climbing turn at full power, to accelerate from zero groundspeed on the north/south line, to 75 MPH south, fast enough inertially, that no loss of airspeed is experienced with the perceived wind change? Yes the wind will contribute to the acceleration, south, but the 'plane does not have a sail on it either. Power is required to accelerate the 'plane from zero to 75 MGS against its inertia. That power is already being used for the turn and climb (and 150's are not known for excess power). On a runway, with zero wind, acceleration from zero to 75 MPH will use up at least 500 feet of ground run. A tailwind will help some, but will not negate the need for power to accelerate the 'plane, taking time and distance. During that time and distance, what had been the low speed climb/flight performance advantage of a headwind, is now the disadvantage of a tailwind, and must also be overcome.
This to me is an open issue. Irrespective of the theories of physics purity in the moving parcel of air, my experience (in the aforementioned C150) has been that if you're planning a low speed turn toward downwind, allow for a period of lesser performance as the 'plane accelerates inertially, to catch back up to the moving parcel of air. Right or wrong, this has been taught and demonstrated to me, and I teach it onward as I mentor. Purists will tell me I'm wrong - perhaps so, but I'm wrong so as to remind pilots to be conservative and safe about performance in a changing and demanding regime of flight.