Splitlines are very likely to cut through urban areas. Since the urban/rural distinction is meaningful in American politics, this has interesting consequences.

I'm not sure "arbitrary" always gets you "unbiased," or "unbiased" always gets you to "fair."

Fairness requires tallying up the numbers of disenfranchised in the new method, comparing it to the old. Splitline will exclude some urban voters from the political process for the foreseeable future, and some rural voters. It's not obvious which group loses more (it's highly contingent on the population distribution). But it's worth tallying up, just to see.

If disenfranchised is really our concern, why not just try to minimize it more directly?

Let's say someone is defined as "disenfranchised" if they identify with a party with no chance of victory, or if they contribute overflow votes that will never be necessary for their party to win the district. If you're in a minority party that gets less than 40% of the vote, you're disenfranchised. If your party has over 60% of the vote, then everyone beyond that 60% is disenfranchised. (We can quibble over the definition, or generalize it for more parties, but let's just assume we have some operational definition approaching "disenfranchised," without any definition, we couldn't evaluate the success/failure of splitline anyway.)

Now just draw all the constitutional district maps, and pick the one that disenfranchise the fewest number of voters possible.

Ok, that may be computationally infeasible. So instead, just have each party draw it's own recommended map, and then pick the one of those offered that disenfranchises fewer voters (using data from the last election, maybe).

[1] A man-made definition is exactly what splitline recommends against, but even imperfect but vaguely reasonable definitions of "disenfranchisement" in this method will tend to be more "fair" (in terms of reducing disenfranchisement) than purely arbitrary dividing lines.