Helgoland, different languages (that includes accents and dialects) are essential to ensuring the preservation of cultures. When everyone speaks the same language in the same way culture invariably erodes, withers and dies.
The other thing that makes the survival of languages important is art/literature/music. The only way to truly appreciate wordcraft in a foreign language is to learn the language. Translation is never the same.
The first part is patently false: People all over Germany speak the same language, but there's a great amount of local traditions, rituals, etc etc that haven't been impeded by the lack of a language barrier at all. Though of course you've moved the goalposts and now want to include dialects... Consider the various parts of the US, then: The differences between the local spoken languages are rather small, but still the cultural differences are vast - so vast that some consider it a historical anomaly that the US is a single nation-state.
I'm not arguing against language preservation, by the way - it hurts me greatly that my mum's childhood language/dialect, a certain form of Low German more closely related to Dutch than to High German - is dying out. But there's no point in putting all those withering languages in formaldehyde, turning them into Latin's rural cousins - language preservation is only sensible when the living (!) culture it is embedded in and a community that uses the language in question in day-to-day life can be preserved along with it. Putting it on life support is linguistic cruelty: It's better to let it die a natural death.
And let's not forget that living languages evolve, too! It seems to me that the whole concept of 'saving' a language is misguided. 'Saving' a language can be just another way of burying it, if understood the wrong way.