> Why is it so hard to accept that domain transfer does not exist.

I think, because, that's simply not true. The question is really "to what extent does domain transfer exist, and how can we exploit it?"

> If kids learn chess for a few years, they won't be better at mathematics. After five years of practicing Violin kids don't find learning a foreign language easier.

If kids spend several years on intentional practice of chess or violin, they're also practicing discipline. Compared to kids who spend these years unfocused, I'm guessing this group will have an easier time learning math or French simply because they have better learning habits.