At the most fundamental level, reparations based on skin color are by definition racist. Many Africans in America have no link to slavery in the US.
People can file a claim against someone who caused them harm. And as you rightly noted, the people harmed and who caused the harm are no longer living. But let's suspend that argument and consider that such claims can be inherited by the descendants of the person harmed and owed by descendants of the person who did the harm.
So, you are saying, Obama whose ancestors were slave owners, should compensate African Americans, whose ancestors were slaves. That doesn't seem fair, since clearly Obama abhors slavery, but that is the argument you are making. But Obama, rich as he is, probably doesn't have the "coin" to pay off these claims. So, you extend your claim to include the government under which slavery took place (deeper pockets).
But the problem is the US government never sanctioned slavery, ever. It could not end it, since it had no legal authority to do so. That would be like accessing all members of the EU reparations for what Germany did in WW2, simply by virtue of them joining the EU. Sounds pretty silly. If the government told the states, if you join, you will be responsible for any bad acts done by any other state in the past, many might have passed. That simply was not "the deal". Even today, if New Jersey goes broke due to its unfunded teacher pensions, other states are not required to kick in. But this cross-state liability is precisely what you are arguing. Other states have no say in what pension benefits, New Jersey offers, nor the responsibility to make good if New Jersey teachers go unpaid.
Since, the American Civil War we have viewed our country more as "one nation", but prior to it, it was simply a "more perfect union" of independent states (the whole reason why states felt they had the right to secede). So, had slavery continued after the Civil War perhaps a case could be made that the federal government with the authority to ban slavery failed to do so, but it did in fact abolish slavery.
Even prior to the Civil War, numerous efforts to abolish slavery failed because southern states refused to make that a condition of being a state in the Union. So, our Constitution never had the authority to authorize slavery or abolish it. And yet, you want to access it reparations for failing to do what it had no authority to do. If the US condoned slavery after the 14th Amendment was passed, then you might have a case assuming one could inherit a claim from an ancestor, but that was not the case. Only after passing the 14 Amendment did the federal government have the authority to act against slavery in any state.
Your whole premise is based on a "modern view" of our country rather than the historical reality of a central government with very specific and limited authority strictly defined by the Constitution.
So, if any derivative claim exists for the descendants of slaves, it is not with the Federal government, but either with Britain for claims arising prior to states attaining their independence or subsequently with those state governments that permitted slavery subsequent to them achieving independence. So, with respect to the US, the only logical claim if one accepts that some derivative rights to make claims exist, is to file a claim with the state in which one's ancestors were wronged.
And then each state must consider if it will entertain such claims. And what compensation is appropriate.
This is very different from the Japanese situation where it was the Federal government that interred US citizens of Japanese descent. Not only would their claim under your logic be with the Federal government, but they were US citizens. African slaves were not US citizens.
The issue is similar to the abortion issue. Why can't family members of unborn babies sue for wrongful death under Roe v Wade. Answer, the government does not recognize them as citizens. The Supreme Court does recognize them as "human".
I am not sure what the basis would be to make a claim against the Federal government for reparations, when it never had the authority to ban slavery since its inception. And when it had the opportunity to change its "Constitution" by adding the 14th Amendment, it did.