Low upward mobility shouldn't be considered a bad thing -- in fact, it's a sign of a functioning meritocracy along with the fact that merit is at least partially inheirited.

Rich people tend to be smart, smart people tend to have smart children, smart children tend to grow up to be rich, and so rich people wind up having rich children. Rich people would have rich children even in a society where all children were taken away from their parents at birth and raised communally.

Add to this the fact that children also pick up financial literacy and values (good or bad) from their parents, and there's your low upward mobility right there. I doubt if the other effects (i.e. rich children inheirit wealth and can often get into better schools) are nearly as important as the genetics of it.