Language is rather more than just a way to exchange ideas. Different languages convey ideas in different ways, which in turn forms and perpetuates radically different world views. Language is a great part of culture, both forming it and being formed by it. When a culture loses its language it will change a lot, losing itself and possibly even disappearing entirely, as cultural artefacts and ideas become less possible to express in the adopted foreign language.
A similar but less pronounced effect appears in language evolution over time. Words that meant one thing now mean a different thing but, also, ideas once held dear can no longer be expressed in any meaningful way, or take a great deal of effort to express and, consequently, become lost or changed until they're unrecognisable.
A good example is the biblical concept of "fear". A contemporary reader, steeped in modern culture, will read phrases that refer to the "fear" of god and assume it means people are meant to be in mortal terror. The word originally translated as fear would these days be translated as respect, but that doesn't quite cover the full meaning of the original hebrew.
Or take any greek text translated to English and look for the word love. You don't know whether that was agape, eros or what have you. Ancient greek has many words that are routinely translated as "love" but which mean very different things, meanings that require one or two sentences or a paragraph to explain in modern English. Cultural context is lost in translation. When a culture loses its language it has to attempt to translate its culture into the language it has adopted, a process that will strip a culture of most of its foundation or turn it into a parody of itself.
The idea of a world where everyone speaks the same language might seem appealing at first, but which language do you choose? Any language you chose will end up destroying much of the culture alien to it. Constructed languages, moreso, for the only way they can survive is by crafting a cultural context within which they can function.
A common language for commerce is useful, but we need to encourage the survival of languages in order to maintain the unique viewpoints they provide.
And I say this as someone who thinks this BBC Alba thing is a pile of patronising, politically biased trash.