Because a single game is potentially unfair, whereas a 2-game match with alternating colours can't be.

Indeed. That's it then, no single games for Line4, but minimum 2-game matches with alternate colours - Fencer, are you there? :)

<Then the solution is simple: when you get over a ceiling rating in Line4, you are banned from playing as black :>

This site basically says that Line4 isn't a fair game to the second player, as perfect play by the first player guarantees the latter's win. Is there something we can do to change this? I know that site refers to the standard 6x7, but there's no reason why their findings shouldn't apply to our 8x8.