Well Martair, it's all been answered above but maybe another analogy would help:
Let's take an aircraft ideally trimmed to a known IAS, with the thrust set to the correct setting for that speed. Now let's carry that aircraft up to say 10,000ft under a balloon and drop it. Due to its stability, after falling a while the aircraft will stabilise and fly level at the planned IAS.
The same aircraft, subject to a loss of airspeed ( which is what happens in your inertial mathematical model ) provided the thrust is not touched, will fall as before and regain its stable speed - provided there is enough altitude. The effect of the wind change is transient and is compensated for by a change of altitude.
Now let's put in a pilot. He can do one of three things:
He can do nothing and let the aircraft fall;
He can maintain altitude but let the IAS drop and trim it to the lower IAS (stall IAS in an extreme case) or;
He can maintain altitude and as a part of his scan maintain IAS (and incidentally trim) by adjusting the thrust appropriately.
The third case is of course the ideal one and yet an extreme wind change, especially if unexpected may lead to the pilot adjusting the thrust too little and too late.
Modern aircraft are designed to fly at a margin above stall speed but older pioneering types such as the some of the Shuttleworth ancients were hard pushed to fly at all and were very close to the stall.
On these types the problem was more likely to arise.
Having said that, wind changes will always affect aircraft to some extent as we see every time we fly an approach in gusty weather - IAS and/or glidepath are affected.