I think I'd have to add "general-purpose" into the mix. Complex proprietary niche languages seem to be able to survive a long time without competition. Especially true when the users of the proprietary language are not themselves computer programmers and nobody has the skill to just start creating competition. (Which is why mathematics does have some open options; there's enough skill crossover to make things like Octave possible.)
Octave is decent at what it does, but nothing in the open source world comes remotely close to Mathematica. Having easy access to it (and more importantly, being able to expect my peers to have the same) is one of the things I miss most about being a student. Wolfram's recent price cut for non-student personal use is alluring, though. Some time soon I might break down and pay for it.
I wasn't claiming it was a replacement, just that it, well, exists. Other proprietary areas don't have any open source competition where the target audience has even less overlap with "programmers".
I consider "being the only thing that serves the niche" a huge advantage. Same goes for "being bundled as the only scripting language for commercial product X" (like AutoLISP, especially before VB support in AutoCAD).
