I have perhaps spent too much time on the math and the engineering of perfect ideal non-gerrymandered districts, and it is a good ideal, and it is not enough.
The Voting Rights Act of 1965 decreed that there shall be a few majority-minority districts in states that had historically discriminated against African Americans by gerrymandering away their ability to get a majority in any congressional district. This of course introduces a different kind of deviation away from what purely 'impartial' districts might be. We might call what the VRA did 'gerrymandering for good' in that it constructed districts towards a specific end, the classic mode of gerrymandering, but for a purpose we call good. We could call it 'electoral reparations'. In an ideal world we would not need this and we would have districts that were compact or guided by enlightened social interest towards representing identifiable regions of people with common regional interest. In an ideal world ideological and identity representation would be handled by a Proportional Representation system. But we do not live in an ideal world. Voter suppression in America, whether by under equipped precincts or by gerrymandering or by the poll tax of voter-id laws, primarily hurts the poor and non-white. I hope that someday we will build a more perfect union, but for now we still need those electoral reparations.