It's more like outlining an electrician's skill set or the training given a Special Forces operative than putting together a martial art. We don't have Death Metal necromancers who can't learn Jazz teleportation because they're necromancers; we have a collection of abilities that Death Metal folks tend to have and a collection of abilities that Jazz folks tend to have.
For example, there's no intrinsic reason why a DMer couldn't learn to teleport someone just as well as a Jazz musician - it's just that he doesn't. Part of this is personal philosophy and goals; what he thinks is useful, what he's willing to spend his time getting good at. Another part of it is opportunity. He learns his magic from other Death Metalers; they know what they know. If he wants to learn transport magic in this setting, he either has to try to invent it himself or try to trick a Jazz man into teaching him. The latter is not only risky, it would require learning to do it the jazz way - which likely involves playing jazz, which in the mind of the indig is tantamount to betraying his Faction. The former is difficult and risky even if it occurs to him in the first place, which isn't likely; in his mind, that's something Jazz people do. Whereas the verser tends to think in terms of "if he can do it, so can I," the indig thinks of other Factions' magic as being somehow inherently different - it sounds to him like you're saying, "if a computer expert can do it, so can an out-of-work actor."
I was skimming the Magic Skills section while I wrote that paragraph about Death Metal magic earlier, so I'll probably start with them. I might do that tonight, or I might end up writing for other threads.
Incidentally, it occurs to me that the Jazz magical profile lends itself to smuggling operations.