I've converted a £10 trash tier quadcopter to run off of 30G wire. Only 5 meters range, and the weight and momentum of the wire cause extremely difficult to control oscillations, but it still flies (badly)! The transmission losses over such thin wires are massive but the way around that is to supply a higher voltage than is required, and include a linear regulator inside the quad to burn off excess voltage when current draw is low.

I specced the wire purely based on the weight reduction I got from stripping out the cameras, battery, and then replacing the main body with a 3D printed skeleton, as the original battery contributed more rigidity than I had realised.

Sounds like you were supplying power. That's unnecessary in this case. Just leave the battery in.

The question is if you can reliably push video down a 5 mile pair of copper wires and send control inputs back up. And the answer is yes, even for an unshielded twisted pair. With the right encoding and enough voltage, you can get GBits down that wire.

I assume copper will be many times heavier and resistance will make it useless at a much shorter distance. Plus, it's many times more expensive.

The TOW missile is guided via electric signals over metal wires, but is much more expensive and less flexible (and probably has a very different flight profile) than drones and FPV drones. More modern wire guided missiles do use fiber optics (Spike, etc.).

I think maybe a copper wire is susceptible to an RF attack?

Copper is indeed vulnerable to RF/EM attack. (shielding makes it a little less so, but adds weight)