Having a distinct culture doesn't necessitate having a distinct language, but having an existing distinct culture in a specific language necessitates preserving the language for preserving it -- even just the tons of literature, poetry, song, etc, in that culture, not to mention worldviews and philosophical outlooks expressed in words, etymology, proverbs, shared expressions, etc.
(Also cultures with distinct languages are also more distinct than cultures with shared languages -- except of course if the languages are close cousins of the same family and the cultures have been co-existing for centuries already. An english speaking China will be a very different culture).
And we haven't even mentioned the Shapir/Worf hypothesis: https://en.wikipedia.org/wiki/Linguistic_relativity
>Even if that was the case, what would be wrong with cultivating a world wide culture?
You mean besides obliterating every existing culture and using it for parts?
Everything that's wrong with monocultures of all kinds and singular ways of thinking and doing things (less evolutionary adaptable, less competition among different viewpoints, poorer breadth of experiences and outlooks, etc)