Remember, you also have to sell the idea to the public, and which is easier to sell: "Trust this complex algorithm built by mathematicians and their fancy computer models who most certainly aren't secretly biased toward the candidate you dislike", or "RECTANGLES! :D"
I don't see any problems with this myself, as long as the algorithms are fair -- what are some downsides of this, though?
But actually - there are two classes of algorithms out there: one can determine how to fairly divide up a state and another measures how unfairly a state is divided up - instead of going full into computers-determine-everything it might be nice to just have a requirement that the result of the election in the state is relatively statistically probable given the proportions of votes for each party. So people could still draw districts we would just have a manner to prove their districts are acceptably fair.
1. There would be a lot of sudden changes, without any real explanation about those particular changes.
2. Unlike now there would be little on-the-ground reasoning to these changes. Districts would be split on random-seeming streets, with no respect at all about residents felt. Now at least you have someone to blame, and we like to have someone to blame rather than "the computer".
This is really less of an unsolvable problem than people make it out to be - it's just that most of the discussion you hear about it is from the political parties both of which benefit from its existence and, especially, the incumbents who have a much more secure seat with careful district drawing to make sure you don't get too many progressives that might vote out a centrist (or ditto on the other side)
1. https://www.scientificamerican.com/article/the-mathematician...