Should a dying language be "saved"? Preserving cultural heritage is all very well, but expending a child's language-acquisitive resources on a language which won't connect them to the rest of contemporary humanity seems far too high a price.
This comment is predicated on an assumption that I'm not sure has a foundation in science: that a child's "language-acquisitive resources" are finite in some way, or that a child learning a minority language won't "have room" for other subjects because of it. Because many, many children in the world speak one language at home and another at school, I'm not sure there is any foundation for this assumption.
There's only so much time in the day. If a child is learning math and science and their main language and other skills for seven hours, sleeps for eight hours, and eats for two hours, that only leaves seven hours in the day to fit in everything else, including play time and exercise.
That's the limit on learning languages. We're only good at our first language because we spend our entire lives practicing it. It takes hours and hours and hours of practice and studying to learn another, even as a child. Double that if it's not a commonly spoken language.
In Switzerland, it might be possible for everyone to speak English, German, French, Italian, and Romansh if you're around people who speak it for your entire life. But if a child is actually being taught these languages, let's say an hour each day... well what time is there left for anything else? Sure it might not push other knowledge out of their brain, but if it pushes other knowledge out of their reach due to not having time to learn other subjects, that's even worse. How much time will they put in learning a dying language, and what other, more useful knowledge could they have gained otherwise?
It's the opportunity cost.