I have mixed feelings about this. On the one hand, yes, it's a pity to see a cultural artifact like a language fade away. I get that. But on the other hand, having the world Balkanized into thousands of mutually incomprehensible linguistic ghettoes is a bad thing, because it makes it harder to get things done on large scales. Things would just be easier if we spoke a manageable handful of languages.
There's a middle road, you know: being bilingual. To run with the Icelandic example, you'll be hard pressed to find someone who speaks it but not English. Where I live, there's also a local language (Frisian) spoken beside the 'bigger' language (Dutch). And here too, lots of people speak English. Or if not, you might get lucky with German.
I think there were almost no advantages to this dialect killing.
Small minority dialects are at a danger of dying out, not crowding out the bigger languages. This is how all of europe worked for hundreds of years. My Grandfather grew up speaking yiddish (german dialect) in school, czech in town & Hungarian at school. These are completely unrelated and individually difficult languages. He later went to college in German & Latin, later on English. He spoke 10 languages in total, most fluently. I knew him in a language that he learned in his 40s. This was normal in his day. They weren't afraid of languages then.
Anyway... if your "home" language is a tiny, local one. There is no danger that you will be monolingual in a commercially useless language. You will speak a big language too. Speaking 2 makes the 3rd one easier to learn.
^more on the dialect end of the spectrum than most people realize.