Many garments are black these days, What dyes are used? Are there other considerations beyond fad and fashion? Is black easy or to manufacture? Does black hold up or last, i.e., '‘wear’'well?
Your first question has no single answer. There are several families of dyes used in commercial fabric manufacture; the choice is in part based on the type of fabric being dyed (plant fibers such as cotton, animal fibers such as wool, and synthetics such as polyester each have different requirements, and silk and other very delicate fabrics may have additional considerations).
Back in the Medieval era, high-quality black cloth (especially black silk) was a status symbol, because achieving a rich, even black color required labor-intensive, and thus expensive, overdying techniques. Once cheaper black dyes were worked out, black became the “basic” color for working-class and everyday clothing because it is good at hiding dirt, which was important back in the day when most outer clothing was made of wool and never washed (seriously; wool clothing would be bushed and aired, and spot-cleaned as required, but typically not completely cleaned until the garment was taken apart to reuse the fabric). Black dyes of the 18th and 19th century were also more durable (more fade-proof) and relatively easy to apply compared to bright colors, which often required more expensive dyes or more elaborate dying methods.
The advent of cheap synthetic dyes changed everything; black has no significant advantages anymore. Nowadays it’s just fashion.
Is the wool from black sheep in high demand?
No. Almost all sheep bred for wool are white; black wool would probably be from a meat/milk animal and would be low-grade wool probably best used for feltmaking or stuffing. You can certainly make cloth out of it, but it wouldn’t be very good quality. Additionally, black wool isn’t really all that black unless you raise the animal in a coat (or indoors in the dark), and with wear it will fade to an unattractive rusty brown.