This logic assumes that none of this benefit is positional. The family moves to a richer area, the kids do well in the fancy local schools, get into top colleges, make lots of money, etc, yes. But a lot of these opportunities look like "each year we take the best N people we can", so there are probably other (less qualified) kids who do slightly worse than they would without the move.
As an analogy, if being in the tallest 5% of society makes you earn $100k more, we would expect a randomized controlled trial on increasing children's heights to have a large positive effect on income. But if we then rolled that out to the whole society those benefits would turn out to be illusory.
This is still valuable from a perspective of reducing segregation and inequality, but I'm skeptical of its presentation as an extremely good deal economically.