Should we preserve dying languages?

A language becomes endangered when its speakers do not pass the language down to the next generation and its remaining native speakers grow older and pass away. A language is considered dead or extinct when it has no fluent speakers. Languages change, shift, and die throughout human history, yet linguists and speakers of endangered languages go at great lengths to record and maintain such languages for research purposes or cultural heritage. If languages change and die naturally, are they worth preserving? What is the purpose of preserving a dying language?