Ahriman
Tyrant
some units could be on the 'long' supply line, some could even be off the supply line altogether.
Having a mechanic that can lead to units being unable to move does NOT sound like a good idea to me. Particularly when used against the AI; they launch an invasion, and then you pillage a few roads and leave their entire army stranded? Ugh.
And having to check a pathfinding route to every tile seems very complex and non-transparent to a player. A player can't instantly look at a tile and see "how many turns" it is away from your cultural borders.
Making exceptions for rivers makes it even more confusing.