I think this is true for what it's worth. If you are naturally talented (or limited), where did the natural talent (limit) come from and why do you deserve credit (blame) for it? If you are not naturally talented and had to work hard for your successes, where did this inclination or ability to work hard come from and why do you deserve credit for it? This seems to reduce to the problem of free will versus determinism. For two identical twins, one ambitious and hard-working, the other indolent and free-riding, what accounted for the difference in behavior? They chose? What made one choose the one path and the other the alternative? Like free will, the idea of moral desert for position in society requires a bit of magical thinking.
Like determinism, the idea that no one deserves anything, while neat, implies no course of action whatsoever.
Material inequality is one kind of inequality among many. Political inequality is more troubling by far, for political power is the power to push people around. Coercion is wrong on its face, and so the existence of political inequality requires a specially strong and compelling justification. However, if the luck argument cuts against moral entitlement to material holdings, it cuts equally against any moral entitlement to political power.
The justification for political power is generally sought in the "consent" of the people through free, fair and open elections. Yet the fact that someone has gained power by a democratic ballot can be no more or less relevant than the fact that Warren Buffet gained his billions through a series of fair, voluntary transactions. John Edwards (who, by the way, is a mill worker's son) didn't deserve his luxuriant tresses and blinding grin. Reagan didn't deserve movie-star name recognition. Bushes don't deserve to be Bushes. Kennedys don't deserve to be Kennedys. Kerry's war medals? Please.
This luck argument can consume whatever argument it might be harnessed by.
If the luck argument is any good, then democratic choice and the resulting distribution of coercive political power is also, as Yglesias says, "chance all the way down." And if luck negates the moral right to keep and dispose of one's stuff, it also negates the right to take and dispose of others' stuff.