In terms of the dielectric difference between a conductive material such as silver or copper and a highly resistive material such as air, why is a DC frequency resisted by air, but a HF signal travels through it? How does this relate to the impedance of a vacuum at Z0 = 376.730313668(57) Ω,

Z0 must not be linear across frequencies otherwise the resistivity of a vacuum would not be as high when a vaccuum is resisting free space?

 

Or to rephrase it, if the impedance desired in a SW system is 50 ohms and Z0 = 376 ohm, should not the systems be designed to match Z0 for more efficient power transmission?

 

if the impedance desired in a SW system is 50 ohms and Z0 = 376 ohm, should not the systems be designed to match Z0 for more efficient power transmission?

A properly designed antenna is an impedance transformer.

From Google:
It is good to understand that an antenna itself can be considered an impedance transformer. The antenna transitions power received from the RF circuitry through the Tx line (matched to an impedance of 50 Ω in most cases) to free space (impedance of 377 Ω).

So the antenna does what you suggested.

 

Or to rephrase it, if the impedance desired in a SW system is 50 ohms and Z0 = 376 ohm, should not the systems be designed to match Z0 for more efficient power transmission?

It is the feed point of the antenna that is 50Ω, not the radiators.

 

I have proided rather much measurements over coils, from smallest to the rather large, having tens of kilovolts and several tens of Amperes inside at 50-100 MHz. Theoretically, solenoid field axially goes via the eternity by means of distance. The practice is that in inc h distance the air is plasmaficated, the two inch the ester is burned off even not connected, the for inche distance is okay to fulfill the ICNIRP health normative demands, the half meter distance the radiated power density falls beyond the local radio-stations power density, at the one meter distance the parasythic emission stays beyond the sensitivity of measurer. Why - because the coil`s impedance is far off from the 376 Ohms.

 

Or to rephrase it, if the impedance desired in a SW system is 50 ohms and Z0 = 376 ohm, should not the systems be designed to match Z0 for more efficient power transmission?

As was said before by @Ya’akov "It is the feed point of the antenna that is 50Ω, not the radiators"

That's why we have antenna coupler/matchers.

https://abracon.com/uploads/resources/Abracon-White-Paper-Antenna-Impedance-Matching.pdf

 

I found [some] of the answer:

"Zfs (space) is resonant at all frequencies due to ε0 (farads/meter) and μ0 (henries/meter). Thus it will have no reflection. Free space is lossless and the signal only gets weaker because the energy spreads out over a larger and larger sphere. The /meter part causes space to develop a resonant velocity (speed of light). But all frequencies resonate in space with no reflection. The antenna matches space with the transmission line."

https://ham.stackexchange.com/questions/17872/is-an-antenna-always-matched-to-free-space-impedance

Present formulation for the Refractivity Index of Air in terms of c:
https://nvlpubs.nist.gov/nistpubs/jres/086/jresv86n1p27_A1b.pdf

 

I found [some] of the answer:

"Zfs (space) is resonant at all frequencies due to ε0 (farads/meter) and μ0 (henries/meter). Thus it will have no reflection. Free space is lossless and the signal only gets weaker because the energy spreads out over a larger and larger sphere. The /meter part causes space to develop a resonant velocity (speed of light). But all frequencies resonate in space with no reflection. The antenna matches space with the transmission line."

How is this different from the answers you were given here?

 

Why an Antenna Radiates https://www.arrl.org/files/file/Technology/tis/Why an Antenna Radiates.pdf

 

Why an Antenna Radiates https://www.arrl.org/files/file/Technology/tis/Why an Antenna Radiates.pdf

That was a great explanation based on retarded potentials.

https://en.wikipedia.org/wiki/Retarded_time