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.
Step
The trouble with this argument is that it also applies to a turn in nil wind. In still air the aircraft and its engine have to accelerate the aircraft from say 75kias north to 75kias south. We dont have any problem thinking that the aircraft can do that without losing airspeed due to its inertia.
What we do is use the lift vector tilted by banking the aircraft into the turn to provide the required acceleration, and a bit of back pressure to increase the lift so that we maintain level flight. This increase in back presuure of course gives us a slightly greater AoA which may be noticed as a small reduction in airspeed (because drag also increases). But thats nothing to do with the wind because there isn't any.
To really convince yourself that for a turning aircraft the wind has no noticeable effect is to go for a flight in a glider (sailplane) on a good thermal soaring day with say a 15knot wind. Get well centred in the thermal with say a turn at say 45deg of bank. The glider will turn through 360deg in less than 30 seconds and the airspeed will be rock steady all the way round. You may hit areas of greater or less lift but these are seen and felt as changes to the climb rate - there is no change in airspeed so long as attitude and bank angle are maintained.