In my opinion (as someone who works in NLP & computational linguistics), preserving more data on how languages can work is the most important bit. Languages do

In my opinion (as someone who works in NLP & computational linguistics), preserving more data on how languages can work is the most important bit. Languages do influence cognition a little bit, but not as much as most people think. Nevertheless, most people think that they do, and if you only know a few languages, its easy to get stuck thinking that, oh, this is how all languages must work, and this is inherently how people think. This is a problem in contemporary linguistics- the "big" languages are really heavily studied and theories are developed to describe them accurately, nevermind that they may completely fail for, say, Xhosa or Straits Salish. The bias has been decreasing over the last few decades, but getting a really good idea of the real fundamental underpinnings of human language depends on all those minority languages not disappearing, undocumented, before we're done. Of course, there are other reasons which are important to people working on other fields- languages are strongly tied to culture, and when a language dies, so does a lot of other cultural knowledge and practice that may be useful to ethnologists, psychologists, philosophers, etc.