A properly made transmission line is just that, a transmission line: it obeys the Telegrapher's equations and transmits power, not purely voltage or current alone.
However, once you start packing all the energy into the EM field between the conductors like that, you depend upon transmission line effects. While it could be handled, it makes things that much more difficult than they already are.
As is, lines are well under 1/4 wavelength, so they can be treated as simple lumped LC networks, and LC networks can be used to compensate for their impedance (such as: line reactors to tune the capacitance, and tap changers to compensate for the voltage drop). And that impedance isn't a terribly large fraction of the load impedance, so the voltage regulation isn't screwed up too badly. Compensation networks (line reactors, tap changers) need only modest tuning ranges (or can be static fixed components), so they don't cost all that much.
You'd also have to control for interference effects. The grid should be a strict tree structure, with no cycles (loops), and carefully aligned parallel transmission lines where extra capacity is needed. Precision, and probably self adjusting, phase matchers would be needed to combine multiple power plants, or to implement loops or interconnect sub-grids. (So, it wouldn't be much of a "grid" anymore.)
The transmission lines themselves would be more expensive, since they have to twist or swap every 1/4 wavelength, or be made in some twisted or interleaved pattern that minimizes radiation. Not to mention [true, resistive] losses due to skin effect, induction in the support structures, radiation and so on.
Strictly speaking, "capacitive or inductive loss" is preposterous, but the implied effect is real: a robust power transmission system should have a low impedance (constant voltage) characteristic, but a transmission line system must be impedance matched -- and as such, no point in the middle of the system will have a low impedance, making the compensation and regulation hardware massively more involved (wider tuning / adjustable range, more control units in more locations, more emphasis on point-of-load regulation, etc.).
Safety may also be a concern. At 50/60Hz, there's a few milliseconds between pulses during which arcs have a chance to cool down and break. This is still not enough on the biggest feeders, but at lower voltages and currents, it helps greatly with safety and fusing. High frequencies would require very expensive fuses; I'm not even sure what technology is used for high frequency or RF fuses. With power pulsating faster than the thermal time constant of even very small arcs, it behaves essentially as DC, very difficult to break.
Presently, DC is in use, but only on individual feeders over very long distances, where the efficiency and capacity advantage is too great to turn down. With the vast preponderance of switching supplies today, it might be tempting to entertain DC as a domestic distribution method, but besides the enormous infrastructure cost of implementing it, it probably just wouldn't be a safe enough idea -- electrolysis and tracking on leaky insulators, static fields around everything (imagine the dust -- and insect and bird -- collection power!), nearly unbreakable arcs (expensive fuses, switchgear).
Afraid I don't know much about references or research concerning the subject. It's an interesting idea to entertain, in a generally useful subject, regardless of its economic or safety drawbacks.
Tim
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