I wonder what the figures would be for families with the same incomes and no inheritance? I would be willing to bet that there would still be a huge difference.
There are several factors besides inheritance, some of which can be fairly addressed and some of which cannot.
It is unfair to state "child X lacks supportive parents, but child Y has them, so we must GIVE child X better grades than are earned." Not only is it unfair to Y, it is unfair to X as well because X now has reduced opportunity to gain from public education.
It is unfair to tax working people into poverty because the government wants to spend more money to address the "issue"
It is fair to provide free education through 12th grade; this is done for all children (save those who opt out) and is generally regarded as a positive investment in the future. It is not fair to bus children an hour each way to achieve some ideal of racial integration.
It is even fair to tax inheritance, though the situation a few years ago was atrocious - those with extreme wealth had almost no inheritance tax, while those with moderate wealth could lose more than they inherited. The last needs some explanation; a father launched a small business, which grew during his lifetime to be relatively prosperous. When he died, the IRS cam in and valued the business at $3.8 million and assessed a total tax on the estate of just at $2 million. His heirs tried to sell the business, but could only get $1.5 million. The IRS seized everything remaining and auctioned it for $150000 then they billed the inheritors for the balance due - $350000. Talk about a farce; the business went out of business and the employees lost their jobs, the family went bankrupt and the government probably lost more tax base than they made up with the seizure. In contrast how much of the Walmart fortune went to taxes?
I have known black people on both sides of the spectrum - a single mother of two who works two jobs (~ 7-80 hours a week) to avoid welfare, and a black woman who had children every year or two and never wanted to work, but claimed she was "owed" the checks because of slavery. Until the latter attitude is eliminated, I doubt the situation will change, as welfare is a destructive mechanism, both for individuals and societies.