I wonder if this is more due to Mercury's orbit being so frequent that it is more often able to occupy that "closest window" while other planets remain further away for longer.
Would this mean the second closest for any planet is Venus being the planet with the second highest orbital period?
My guess is that as long as the orbital periods of the involved planets are sufficiently different (not being rational multiples of each other for example) , making the system ergodic . Then Mercury will always be the closest by the metric.
