for the wind to affect the speed of an airplane so much, we need to observe it practically.
You mean by like, determining the wind and then seeing if it affects a plane?
For example, does the maximum speed increase by 20% when driving a vehicle
A car operates in a fundamentally different way to a plane.
Cars drive along the road. They control their speed by the speed of rotation of the tires.
People also moderate their speed when driving.
Planes fly in the air. They control their speed by moving air from in front of to behind it. They have a maximum efficiency based upon their airspeed.
If you want a practical example, try it with a toy plane or copter, one which doesn't use GPS or FLOW to maintain position.
For example, a cheap toy quadcopter.
If you get one, you will notice that in strong wind, even if you try to go against the wind at full speed, it will still end up going backwards, with the wind. Then if you try and have it go with the wind, it will go much faster. And if you just have it hover, then it will move with the wind, slowly drifting.
If you use one with GPS to maintain its position, then something else happens. The simplest example is telling it to hover. Instead of hovering and getting pushed with the wind, it tilts into the wind to try to move forwards, with the wind then pushing it backwards, resulting in it remaining in place. The stronger the wind, the greater the tilt.
So it is easily observed practically.