The world is already homogenizing due to technology - media, transportation, communication, etc. The discussion that needs to happen is: Is homogenization a bad thing? Would losing parts of cultures really be that bad for humanity? Would it be worth it for the entire human race to be unified in a single, global culture?
If you think about it, despite the idealism of preserving cultural identities and keeping traditions alive, most of the major conflicts of the world throughout history have been between - and largely due to - different cultures. Just look at the huge conflict between ISIS and Western civilization right now.
Language unifies - but it also separates. Ancient Rome referred to the Germanic tribes and others as "barbarians" and looked on them with contempt simply because they did not speak Latin. That was actually the root of the term "barbarian", coming from "bar-bar", the equivalent of today's "blah-blah-blah" - referring to the way their language sounded to the Romans. One of the issues with illegal Hispanic immigration in the US is the language barrier and the fact that many immigrants don't learn English. It limits their options and their ability to contribute to society and so paints a negative picture for native English speakers.
A common language certainly won't solve everything, but it's a step in the right direction. And it certainly won't stay the same forever, but it would be more stable than the languages we have now. We can see even now that languages are far more stable than in the past, where the language could change slightly even from one village to the next (despite being one "unified" nation, Spain actually has 3 separate languages). With a governing body to regulate a new language, it would stay stable for a very long time, especially with regards to its structure and grammar.
And don't forget - there has never been a language that was "created" by a group of people who set out with the intent to do so. All languages have gradually evolved from other languages through dialects and vernacular in particular areas. All of them inherited inconsistencies and arbitrariness from at least one, and often many (looking at you, English), other languages.
A language that was crafted by a group of specialists with the intention to last indefinitely and fulfill all of our communication needs could endure for a very, very long time.