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.