No one argues that a transmission line needs termination. The question is what constitutes a transmission line. The general rule is that the length of the line needs to be comparable to the wavelength of the signal transmitted. That is why impedance matching only becomes an issue at higher frequencies (shorter wavelength).
Nope. The general rule is, what the source "sees" when it is going to leave a signal. If you put a wire into thin air,
then it will see the impedance of free space, around 377Ohm. If the Impedance of the source is different from that,
which is mostly the case, then it will come to distortions caused by reflections. If you put a piece of cable with the
impedance of 50 Ohm to the source, no matter how long it is, then the source will "see" these 50 Ohms at first.
If the impedance of the source differs from these 50 Ohms, you'll have reflections, distortions etc.
That is why the impedance of the source should match the impedance of the transmission line, which is seen
by the source at first.
Assuming the transmission line is homogen all over and it hits the end, then the same will happen as at
the beginning.
Therefore: no matter, how your transmission line is looking, if you want to avoid reflection and distortion, then
you have to follow the rule:
impedance of the source = impedance of the transmission line = impedance of the target.
This is independet of the length.
For this reason we have antennas. They adapt the impedance of the source to the impedance of the target.
In ideal cases you have a SWR of 1:1 which means that nearly all of the energy coming from the source will
reach the target. No reflection. No distortion.