Fantasy fiction's depiction of arms and armor is often ahistorical, sometimes outright anachronous (and why not, when you're talking about a purely fantasy setting?) The idea of an x-shaped leather harness (which in the older literature means simply "armor," or sometimes "armor and weapons") that has straps over each shoulder with no underlying coat, plate, or mail is fairly impractical as armor, and probably didn't exist as such. However, historical warriors did need some way to carry their gear and attach their armor, which led to items like the "Varangian bra" - probably not what Edgar Rice Burroughs was imagining, but this kind of infrastructure were definitely a component of ancient armors, which could include leather straps that cross the chest. Really, the He-Man and John Carter examples look closer to ceremonial pectorals than functional armor.