Right, it's fundamentally different for other reasons. For one thing, no two "installations" of a natural language are identical. The natural language learning process isn't like loading a program into a machine, but a "reverse engineering": forming a refined set of hypotheses about what the rules are, from examples. Thus after years of learning, still no two competent, even native speakers will agree about all the fine points of what they learned.
By contrast, we can easily install the same version of a programming language interpreter/compiler and run-time onto countless machines and get the same behavior. The machines do not have to guess what the language is by forming hypotheses and testing them against more competent "speakers", to obtain either approval or correction. They just receive a ready-made software image.
In essence, a million installations of the same programming language are just manifestations of one image, whereas a million speakers of a language are individuals (not just as people, but as speakers of that language).
If people could receive a language as an image dumped into the brain, it would be a game-changer. It would still be a game changer even if it took five years to complete, rather than an hour. It would make fledgling languages more viable.
Because languages are hard to learn and even harder to learn very well, people tend not to be so interested in fledgling languages that can't be used outside of a small locale with a small number of speakers. Not as a second language, that's for sure.