Norm Geras semi-refutes the "reducing inequality benefits us all" argument:

To say that even those at the top of the proverbial heap (should) have some interest in reducing inequality is not the same thing as saying that that is what is dictated by their 'naked self-interest' when all is said and done. They have some interest in it, yes, because they too stand to benefit in various ways from the alleviation of social problems. But by being made relatively worse off in material terms through the reduction of inequalities they also stand to lose certain benefits....It's too quick to conclude that the balance of [their] interests must lie in one direction rather than the other.

That's not to say we shouldn't favour reducing inequalities. We should. But arguments from morality and social justice still matter in explaining why. I wouldn't be counting on the self-interest of the very rich to do all the work.