bookworm
That's an interesting way of looking at it. I am not qualified in this field so better not say any more, but I feel that a better way to look at it is to start with an assumption that two planes are already inside a sphere of a given radius, say 1 mile, and work out if they are more or less likely to hit depending on the rules they follow.
Anyway, the French use the semi rule, which appears to discard half of whatever advantage there is.