I wonder if an electric plane could be fed power via the control lines and run for days?
I note that there have already been functional roundy-round airplanes that worked as described, using dry batteries, 50 or more years ago. They weren't impressive as far as performance, but would fly level as long as you keep putting in new batteries.
I doubt that you can find insulated lines that will carry the amps to fly a modern plane at all.
Maybe a little toy on 10' lines, but that's about all.
Are the cables coming off a Lipo really necessary? If so, good luck.
Of course, for power through the lines, you would jack up the voltage to reduce the current, so you could use smaller lines. If all you were going to do was fly round-and-round, you might need 100 watts or so, for a 6S pack it would need maybe 4.5 - 5 amps. Put 5 of them in series, you cut it to an amp or so, you can run that through 24 or so gauge wires if you have high-temp insulation. You only need one wire to be insulated, so for this limited purpose, seems workable in that respect. Too much drag/weight, run the voltage even higher.
Electric cars run at 400ish volts, for similar reasons.
Brett