What you're describing is revenge. It's not exactly conducive to a peaceful society. The times in which the average white harbored racist thoughts against people of color in this country are over. Therefore it's not only useless to punish people who mean no harm for the sins of those who came before us, it's damaging because that may spark truly evil thoughts of revenge. This would widen the racial gap, not act as the catharsis you seek.
I get it, a lot of our history is lousy. But there is no way for blacks to avenge themselves without causing far more pain and suffering than they would solve.
Basically, I want people to realize that there are no sides. Most people don't see skin color anymore, only fellow human beings. If someone of one race decides that another person of another race needs to "pay" and their only known crime was being white, or black, then that person is acting on racial prejudice alone.