I agree with parts of what you say but not others. This debate is largely based on value judgments.

Agree that keeping culture for the sake of culture (tradition) is not worthy, but neither is changing arbitrary cultural values for other arbitrary cultural values.

Cultures that border each other will always exert influence on each other. This of course will change both cultures but the change can be based on factors the respective cultures can weigh as beneficial to themselves. Vaccines and science for instance can be a cultural crossover as the receiving culture can weigh the benefits to their own interests.

I do not see a single language being in favor for the cultures assimilating to it but rather for the core groups benefit.

Ease of governance for instance. Ease of capitalistic endeavors, which almost always favor the established core rather than the peripheral cultures in terms of what they value. Companies don't hire people to help those people but because it benefits the company to do so. Hard to tell many people in Bangladesh for instance their situation has their best interest in mind.

Speaking different languages is horribly inconvenient in the globalized world. 

Being a mono language speaker is terribly inconvenient. It is more likely that creoles or multiple languages will be spoken rather than a single language. Language is not static and geographically isolated from many influences other speakers will be subjected too. This is in line with your point about dialects. A world wide language seems highly improbable without pockets of large variance within that language.

Shouldn't this be on the other side of the debate?

I honestly don't believe that the loss of a language leads to loss of culture, ...

I am not sure linguists would agree with you. The idea of linguistic relativity notes that language is how we frame our realities. This of course allows us to interpret our reality in a preset ever evolving frame of cultural reference. Language of course has to have shared definitions with its users. If the only words you learn for something belittle or ridicule that something this is your first and sometimes only frame of reference to the issue.

On personal levels there will always be some leeway but on the cultural level it is more persuasive. A corallory to the to this idea is that the more important something is to a culture, the more words that culture has to describe that something.

A common example is the number of words Inuits have for snow, being well over 10. To many others there is only a few.

When doing translations there are sometimes words that do not have an equivalent word in the other language, or it may convey a similar idea but slightly different like the Inuits and snow. Googling this idea brings large amounts of results. This is why languages that are in close proximity usualy have loan words. Unless the new language is somehow impossibly inclusive of what is important to specific cultures it will limit the rhetoric of those cultures in those matters.

Your example of English being dominant is correct, it is the worlds lingua franca concerning business. It is very common that business minded/capitalist cultures learn English for obvious reasons. Another example of this idea, can you name how many words the English language has for currency?