Many people around the world speak English, but they don't become culturally American or British because of it.
Actually it kind of does of does;
https://www.economist.com/blogs/prospero/2013/11/multilingua...
https://www.sciencemag.org/news/2015/03/speaking-second-lang...
https://www.psychologytoday.com/blog/life-bilingual/201111/c...
https://www.edge.org/conversation/lera_boroditsky-how-does-o...
At the very least having multiple languages ensures a diversity of thinking.
Then an Englishman asked for my John Hancock.
[An individual’s experience is built entirely in terms of his language.]
The strong hypothesis says that language determines and bounds your thinking, the weak hypothesis is that it influences and conditions your thinking.
https://www.ted.com/talks/keith_chen_could_your_language_aff...
It's really unclear to me that much harm will be done if everyone speaks the same language, and it's clear to me that there will be great benefits. That's an easy position for me to take as a primary speaker of the world's dominant language. It's also no skin off my back if other language groups wish to continue maintaining their own languages. But I guess that those which aren't strong enough will fade over the centuries, as many already did in the past.
This is even true in math. Based on the set of axioms you allow, you can prove certain facts. A math with different axioms may have completely different theorems, and some observable real world behavior can be better modeled under one set of axioms than another.
Language could be described as a math for personal expression and everyday life, and each language has its own axioms and theorems.
I am very skeptical that this happens commonly, or that the necessary terms couldn't be ported over to the common language if needed.
> Why can a man never starve in the Great Desert? Because he can eat the sand which is there. But what brought the sandwiches there? Why, Noah sent Ham, and his descendants mustered and bred.
Look at the less forced genres of music. Rap in the USA, Grime in the UK, similar but different. The UK has a very different type of indie (named from coming from an independent label) music. And Country is only popular in the USA.
If you have a quick look on the surface it can be similar, but if you look deeper, where it matters, then the variation is there.
That said, I do think having more languages is better, a more diversified ecosystem is more likely to survive. And from my point of view, it's more interesting to live in.
American rock has its roots in Jazz and Bluegrass, which has its roots in the African slave diaspora. Japanese Visual Kei was influenced heavily by American glam rock bands. Does that mean Visual Kei merely an imitation of American culture, or that it expresses the same things that American rock does? Of course not. You can borrow the sound and the style but still make something culturally unique.
K-Pop is probably more "Americanized" than Japanese pop, but it's still distinctly not American. I don't think anyone would confuse either Japanese or Korean culture for American culture, even though both incorporate Western aesthetics and English into their cultural expressions.