Within one language there is plenty of jargon and it constantly developes to fit the needs of the user.

This always happens with cultural, people confuse the function of a language (to communicate) with something special in of itself.

A good example is theater, theater used to be the dominant form of long form narrative entertainment, it was one of the best ways to satisfy the need people felt for this kind of entertainment. Now it's movies, or even tv-series. Poetry used to be very popular, now we moved on. How do you know that innovation is driven by different languages? The lingua franca of science is English and the majority of innovations are published in English.

If 10 people in a room all speak the same language, 10 people in the other room speaks all different languages, which group has the best chance of trading ideas?

Innovation comes from the the mixing of ideas, this is best understood if people can understand each other. Science would not be were it is if there were not a common understanding, that's actually one of the first thing you learn. Jargon, you learn the language of your discipline, to better understand previous knowledge and to communicate your ideas to others.

If my teacher or professor speaks a different language than me, how does that foster innovation? It does not, cooperation comes from understanding each other, not not understanding each other.