Do languages have value because they exist?

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Steven Bird at Language Log talks about Usarufa, a language of Papua New Guinea that is in danger of dying out. He wanted to pass on the seriousness of the language's fate to its native speakers, so he turned to an audio aid.

I played them a recording of the "last words" of the Jiwarli language of Western Australia. After some questioning looks I explained that this language is now dead, and we were listening to its last speaker before he died. As one they all looked down, shaking their heads in disbelief and saying sorry, sorry, sorry…. It was as if I told them a mutual friend had died. They urged me to put that recording on a cassette tape so they could take it back to their village. That way, everyone would surely understand what will happen to the Usarufa language unless there are serious attempts to revitalize it.

This story struck some readers of the Language Log as especially poignant, and it elicited such comments as this:

Thank you for this! I'm often struck by how apparently uncomprehending many people are about the gravity of language death.

And this:

The technique you’ve discovered seems to be effective in conveying the gravity of language death to people, and I’d recommend it to anyone else who has trouble convincing a group whose language is endangered.

And this:

This made me a little weepy.

These reactions prompted me to pop into the comments section and say this:

I understand that many people, including non-linguists, think it is a bad thing that languages die out, but why do they take it so hard? Is it simply an emotional gut reaction? Does a language — any language, including English — have an intrinsic value simply because it exists? Or, if it reaches the point where there are no more native speakers and it loses its value as a tool of communication, is it just as well that it passes into the realm of history?

I'm not saying this as a troll. I'm truly curious because, even though I appreciate the beauty of well-written words, I also realize that languages die out from time to time, and I don't think humanity is the lesser for it. In fact, we continue to reach for the stars, to better ourselves and our neighbors, and to make grand new discoveries. Think of me as insensitive if you like, but I wonder why the death of a little-used language always so horrifying.

What do you think? Is the death of a language always a horrible thing? Do languages possess a value because they simply exist? Or is a language a neutral tool that is used to pass on information, and when that tool is no longer needed it can be cast aside without emotional attachment?

I'm truly curious.