Take a transmission line like a coax line with an air dielectric. The wave that propagates down this line is a TEM wave. The wave impedance of this line is 377 ohms.
If you're implying that because the dielectric is air the impedance is 377 ohms, that's not true, I'm afraid.
The impedance of a coax cable is given by:
Source: Wikipedia.
Where
D is the internal diameter of the shield,
d is the diameter of the internal conductor and
εr is the relative permittivity of the dielectric (you can consider it 1 in the case of air as a good approximation).
You can obviously have a coax with Z
0 = 377 Ω, but you'd have to choose D/d to be around 540.
Commercially, coax cables are 50 or 75 ohms. Depending on the dielectric you use, that relation would be in the range of 30 or thereabouts.
Otherwise your explanation is very good. I'd like to have that power of synthesis.