You wouldn't have to wipe away the differences, but for some a "just" society should view someone who had poor parents, limited opportunities and an IQ of 70 and someone who had every opportunity, great parents, and an IQ of 130 as equally important and valuable. Such people view a society where the top 2% of the world owns over half the wealth and much of the world lives in absolute poverty as a sign that maybe our institutions are a bit out of wack.
Personally I'm more a fan of smaller "nudge" (nudge.org) like concepts combined with a progressive tax code and a strong commitment to helping minimize "brute luck" (being born to poor parents) while holding people fully accountable for personal decisions or "option luck" (choosing to take a risk, or making a life decision such as being a teacher vs. an i-banker; or going out at bars instead of saving). (Sort of in a Dworkin fashion see: http://en.wikipedia.org/wiki/Ronald_Dworkin#Theory_of_equali... / or http://en.wikipedia.org/wiki/Luck_egalitarianism).
About half of US workers don't pay income tax. They pay for part of their retirement (SS for them is a modest deal, because their ROI is subsidized by folks who pay more).
Our vice president said that paying taxes is patriotic. Shouldn't they be patriotic?
In any case, there's no need to sit here and think up a priori explanations for this correlation. I'm afraid I don't have time to look them up right now, but I would guess that there have been studies done that examined the performance of adopted children of wealthy families, and I strongly suspect that these studies show that the adopted children perform comparably to biological children of wealthy families.
For such an explanation, I'll note that as the article mentions re. savings plans, much of the behavior which perpetuates poverty tends also to be associated with a short time horizon, or a high discounting of the value of future income. It may be that these practices are largely adopted for lack of educating and training the child of the alternative: that sacrifice and current effort can lead to greater happiness over time. Parents would be well-situated to impart such a lesson.
But my explanation need not be the only factor at play, it only serves to show that the view that income begets income (and thus needs to be equalized) is not the only conclusion supported by the facts.
An alternative explanation is that wealth doesn't beget wealth, but rather those with the characteristics which lead to the acquisition of wealth also beget offspring with the same properties. This isn't necessarily unjust, as Yglesias states, but rather an artifact of the reality of genetics, upbringing and their effects on productivity. If so, to achieve the "equal opportunity" you seek, you must wipe away these differences in both genetics and upbringing, in which case, just call me Harrison Bergeron.