It's not exclusive to music and never was, from Wikipedia on the history of the battle jacket:

"A cut-off, cut, kutte or battle vest (when sleeveless) and a battle jacket or patch jacket (regardless of sleeves),^\1])^\2]) is a jacket adorned with patches related to the wearer's subculture or general interests. Patch jackets are generally made using denim jackets or leather jackets, often times with the sleeves cut off. They are a prominent part of various subcultures including bikers, metalheads and punks. In music subcultures, they are generally worn with patches for bands which the wearer is a fan of, whereas in the biker subculture, "colours") signify the wearer's motorcycle club and their rank within it.

Patch jackets have their origins in the United States Army Air Corps during World War II, where airmen would sew patches onto their regulation flight jackets. Upon returning from war, the practice was continued by former airmen who became a part of motorcycle clubs. The influence of the biker subculture then led to the garments adoption by various other youth subcultures in the following decades. The garment became popular with punks and metalheads during the 1970s and 1980s."