How? Usually pride comes from successful accomplishment or some other validating merit, not simply the virtue of being related to someone/thing. And when you look at the history of people with records extensive enough to trace, most of their accomplishments aren't things to be proud of.
On top of that, usually being proud of your culture/ethnicity carries with it certain obligations of propitiation and loyalty, in particular the greatness of your culture over others by emphasizing your accomplishments and the failures or shortcomings of others.
How exactly does that work? If you acknowledge your heritage, then it has an effect on your self-perception, which influences the choices you make and the beliefs you have. And that is how traditionalists can guilt trip people into doing things that have long-term consequences for short-term ideological satisfaction. And even if somehow you could manage to do what you suggest, there's no guarantee that your descendants will be as open-minded. If history's any teacher, they'll regress to their more primitive, hostile tribal perceptions armed with modern technology and an agenda to avenge past grievances, usually ones that have an emphasis on dishonor or insult.
The only way to escape the fallout of the past is to sever the ties with the traits that influence us to relive them.
Point taken, but Haley had a good reason...African descendants had little to no written history and the documentation of their abuse and oppression was deplorably scarce. By writing Roots among other works, he brought attention to a cultivated cultural ignorance largely brought on by strong adherence to ethnic pride and identity...which led them to exalt themselves at the expense of another culture. THAT is the cost of heritage, and his work sought to help people learn from those mistakes and fix the flaws in society.
Ethnicity and heritage are simply too dangerous to keep around. They are additional stratification tags that over time, provoke resurgences in nationalistic and ethnic purism movements. While they don't have to be as organized and violent as Nazi Germany, we see pocket movements of similar mindset the world over, including America. Because heritage carries with it an inflated self-important heroism, however dormant, that always draws people back to primitive ways and/or views, and we see ourselves and each other in terms of opposition or by how closely they ritualistically exhibit their loyalty to the group. And this kind of group unanimity preys on the most vulnerable parts of the human mind, making us capable of minor and major cruelties and barbarism in the name of honor or sacred.