In most countries you just hire some officials as part of an independent agency and tell them to create reasonable districts based on geographic and social groupings, and it works fine.

I'm not sure if the problem is that the polticians are afraid of giving up the power to control the districts, or if the extremely adversarial nature of American politics means that Americans mistrust their goverment and their fellow citizens so much they don't believe that the possibility of that government making non-partisan decisions even exists.