Professor Taylor, you are obviously educated and sophisticated;  in short, a highly-evolved human being.  Unfortunately, most of the world's billions of inhabitants are far more primitive. Your proposal, to hold persons accountable for actions in which they personally took no part, is dangerous when seized by primitive individuals.  The results of "the sins of the fathers" creed are all too evident in the Middle East, Africa, Pakistan, Northern Ireland, SE Asia, and possibly the former US slave states, to list but a few.  In its most basic statement, the idea is this: your "people" (ancestors, ethnic group, religious congregation, race, nationality--whatever) harmed me, or my people. Therefore, you are accountable, and I may now punish you, and others of "your kind" for those transgressions.  I don't understand how any rational person could find this fair or just.  If someone wearing a green shirt assaults me, am I justified in blaming any and all who are similarly dressed?   By your logic, I might be.
But beyond questions of basic fairness, this thinking can, and does, lead to violence and to such atrocities as ethnic cleansing and genocide.  By way of example:  if I know that a certain group holds me, my children and my children's children accountable for an evil act done by my great-grandfather, I have every incentive to regard members of the group with intense suspicion.  Then, if my worst suspicions appear to be confirmed by a perceived threat, I might decide that to save my people, it is necessary to marginalize this group politically (denying them voting rights, e.g.), or to drive them from the area in which we live (economic isolation, segregation, or outright ethnic cleansing), or--should these measures fail--by mutilating or killing them.  At this point, I would certainly be aware that now their people will blame not only me, but all of "mine" for what has happened.  Logically, therefore, the solution might well seem to be to kill them all--every man, woman and child--in order that there be nobody left with a grudge against us.  From an evolutionary perspective, ethnic cleansing and  genocide are highly predictable responses to the "sins of the fathers" ethic.
As to the question of "reparations", let it go.  Generations ago, slave owners (i.e., white people) did a gross injustice to Africans (i.e., black people) seized and delivered into slavery by Arab traders.  All of the people who were involved in any part of that system are long dead.  Furthermore, the system itself ended well before the majority of present-day Americans' ancestors arrived on the shores of the US.  There can be no claim under any guise against these descendants of later immigrants--unless the "green shirt" example actually makes sense to you.  Although the justice system of the US is undoubtedly flawed, its goal of holding accountable those who have actually transgressed is far superior to prosecuting the transgressors' descendants, along with anyone who looks like them, worships as they do, hails from the same part of the world, speaks the same language, etc., etc.   Have you actually done the necessary research to ascertain exactly which "ancestors" were slave holders?  Or who the "descendants" of these slave holders actually are?  It seems to me that you are putting forth a blanket indictment of all white people in the US, regardless of whether their ancestors lived in a different country until after 1865, or were indentured servants themselves, or were, in fact, devout abolitionists.  
At this point, I confess that I am feeling like I am rising to the bait.  But I can assure you that I, as one of seven children of high school-educated parents, received no "wealth" from my parents.  I went to college, working my way through, with little more than the clothes on my back.  My parents did not, and in fact could not, provide me with cash to go to college.  I can honestly say that I earned everything I have through the sweat of my own brow.  Which brings me to my final comment:  whoever our ancestors may have been, we (the 99%) have a lot more in common than you believe.

SuzieQ45:
I actually don't support reparations personally, partly for some of the reasons you lay out.  I think we do a good job of sorting through the issue on the episode, so be sure to give a listen, when you get a chance.  My own thought about reparations is that it is a bad way of framing a real issue, that can lead, in the hands of more "primitive"  thinkers, to use a phrase of yours, just the sort of mistaken reasoning you outline.   A better way is to think in terms of justice -- all kinds of justice, distributive justice, compensatory justice, etc.    Basically if we look at the effects of the past on the present from the point of view of justice,  we can see the past as having the effect of something like  a lottery.  But sometimes the lottery is rigged.  And sometimes jusstice  demands that we pursue policies that make up for the results of a rigged lottery.    If we think of it in these terms, we get away from us thinking in terms of one person or group  of persons paying reparations to another person or group of persons on the basis of what some long dead person or persons   did or didn't do to some other long dead  person or  persons.    We don't really need to trace  lines of descent from past to present to figure out who owes what to whom as a matter of contemporary justice.   We just need to figure out how best to ameliorate the contemporary effects of the rigged lottery.

I think it is best to learn from our past, and that is reparation enough for me. =

Regarding original sin, the thing about it is that according to Christian theology, before you can get into Heaven you have to be a sinner first, then you have to repent. That's why God has to provide us all with a sin of some kind. It wouldn't be fair to leave some of us out of the game. Original sin is a convenience afforded us by the Holy Maker just in case we don't have anything else to fall back on.

Scientists of European ancestry developed drugs to treat HIV-AIDS that prevented possibly hundreds of millions of Africans from dying prematurely. Perhaps others can think of one or two other positive contributions people of European ancestry made to Africans and humanity in general. Do those positive contributions subtract from their ancestor's sins when we compute who owes what to whom, or should we harp only on the sins and pretend the positives don't exist?