"So, basically, for a Future like Star Trek to work, the heritage of our ancestors has to die."
Not die, just subjugated under the common good. Remember the eugenics wars of TOS and the 'post atomic horror' of TNG were examples of the acknowledgement of humanity to nearly be wiped out to get rid of the more extreme elements. Then humanity needed to wake up to the common need to survive and with the arrival of the vulcans that many of the old arguments were petty in regard to a wider universe. The old beliefs didn't die but were placed in context of a wider view instead of being the only view.