Is Matlab an exception to your statement on programming languages? They are following your hypothetical of owning the only implementation, and people are certainly willing to pay for that proprietary language + implementation rather than use another. Arguably being a somewhat niche language makes its market and competition smaller, but it's a very large niche, spanning several industries and many academic institutions.

Alternatively, Matlab may succeed because it straddles a couple of different categories. It could be argued to be a language, an implementation of that language, a development environment... since it's very goal-oriented, it could even be seen as a more traditional piece of software with an unusually hard-core scripting language.