So in my world it is the future and ALMOST ALL NATURAL METALS are gone. They needed power to get delivered in some form. One scientist thought up a solution: Human hair.
The science community was torn as to if it would work or not. They give their reasons as to why it would, or why it wouldn't work.
Now I ask you, the community, whether it would work or not.
(I don't know the answer so this determines the outcome of this part of the story.)
Under the right conditions, anything can be made to conduct electricity. However, the value of that conduction varies greatly.
Naturally (as @AlexP) states) hair is an insulator. A very high frequency, very low amperage signal could be sent via a length of hair, but you've asked to deliver power. There isn't a way to deliver enough power to operate a simple LED without burning up the hair.
To be honest, almost anything would work better. Salt water would be my first choice. Saliva would be mediocre, but it would work. Blood would work better than human hair. so would aqueous humor. Even your skin would work better (under the correct conditions, you can hold a fluorescent tube in your hand and stand next to a wireless voltage source and the tube will light up).
But considering everything on the human body, the only thing that would work worse is finger and toe nails.
Research shows: Title: Physical properties of alpha-keratin fibers Author: Feughelman, M
"with 7% water content have a resistivity 3 x 10^12 ohm-cm at room temperature"
This makes hair a very bad conductor, but an even worse insulator. In addition, its electrical properties vary wildly depending on the humidity, health and age of the donor, their diet, etc. But none of the variations make for anything really usable.
The closest approximation to utility would be brine-soaked hair, which is a moderately bad conductor. But cotton thread in the same state would be stronger, less prone to degradation, and conduct just as well/badly.
Instead, just use saltwater pipes. A simple brine has a resistance of about
2 ohm per m.
This is still pathetic, and nowhere near as good as copper (1.68x10^-8)
But it will suffice for sort distances.
Of greater concern is how to generate your electricity in the first place. All of our electrical generation methods rely on magnetic inductance, in metals. (some slight exceptions from eg. solar power. But that would still require metals for the conduction of very low voltages from the cells)
Besides. If all metals are absent, just what are the plants and animals using to transport oxygen? There will be no copper for the chlorophyll, no iron for the hemoglobin.
Humans need a role in this future world.
I propose that in your future, humans are largely irrelevant. Artificial intelligences can do all the things humans used to do. They are better engineers, better chefs, better governors, better mothers, better lovers. Humans are cared for by their creations but biological humans are no longer essential.
But humans can grow hair. Just as metals have been exhausted, so too our fellow vertebrates are gone. Except for naked mole rats. We are the only ones left with hair and so that is what we bring to the table. Hair is used as the integral parts of machines - as conductors, resistors, capacitors, transistors, quantum dots; all hair. Humans cultivate their hair for different uses - my hair might go to make microchips, while yours is better suited for tensile struts in air vehicles. When I play a video game, I brag to my friends that some of the components were probably made using my hair.
The artificial intelligences know that hair is not the best thing for these applications. But they were created to care for humanity and they know that humans need to feel needed, and so the use of hair technology continues.
This would, of course, be the kind of science fiction that is actually social commentary.
