Taking your argument to the extreme, if there was a planet that somehow brushed by extremely closely to Earth every thousand years, that planet would be the closest neighbor? I would argue not. I think the average is more meaningful.
I would argue that MOST people would disagree with you and would say Venus is our closest neighbour but once every 1000 years wobbly Erebus returns from the dark to scare the hell out of us.
Mercury is the closest planet on average, but calling it the closest neighbor is just confusing.
When I think of 'neighbors' in the context of the solar system, I am generally thinking of neighboring orbits. It would be hard to argue that Venus's orbit is not the closest orbit to Earth's. Or at least it would seem silly to do so.
Maybe I'm being overly pedantic here, but my view is that orbits have neighbors, and planets have orbits, but planets don't necessarily have neighbors. Something in the word 'neighbor' implies persistence to me, so I don't really consider average-closest planet to be a neighbor when exactly which planet is closest to any other changes constantly.
https://www.merriam-webster.com/dictionary/neighbor
So I guess that means venus's orbit is our closest neighbour, but not the planet itself most of the time....
That's why we say "next door neighbour"
Similarly, the entire area earth and Venus clear with their orbits is the planet’s “home”, therefore, we only have two neighbors, Mars and Venus, and Venus is probably the closest.
Maybe you could say that the orbit is territory that a planet roams, like a nomadic person or migratory bird.
The average closest planet would be useful for regularly traveling between two places.
The closest at any one time is useful for planning intermittent trips.
Let's say we had to pick 2 equal planets we would travel to. Adding the stipulation that planet A is closer on average to HOME than planet B; Planet B has the shortest distance to HOME.
If travel is cheap then planet A is more useful to travel to since you can afford to do it regularly.
If travel is expensive then planet B is more useful since you can't afford travel all the time and rather need to make sure each trip is worth.
If you live in a city it's more reasonable to go to the grocery every week.
If you live in a rural area it's more reasonable to wait for the Shwan truck (type of grocery delivery) once a month.
https://solarsystem.nasa.gov/asteroids-comets-and-meteors/co...:
“Halley's orbit period is, on average, 76 Earth years. This corresponds to an orbital circumference around the Sun of about 7.6 billion miles (12.2 billion kilometers). The period varies from appearance to appearance because of the gravitational effects of the planets. Measured from one perihelion passage to the next, Halley's period has been as short as 74.42 years (1835-1910) and as long as 79.25 years (451-530).”
“During its 1986 appearance, Halley's nearest approach to Earth occurred on the outbound leg of the trip at a distance of 0.42 AU (39 million miles or 63 million kilometers)“
(The orbit of Venus is at about 0.7 AU, so 0.3 AU from that of earth, so that was further away than Venus can be to earth (https://theskylive.com/how-far-is-venus))
It can get a lot closer, though. From that nasa.gov page:
“The comet's closest approach to Earth occurred in 837, at a distance of 0.033 AU (3.07 million miles or 4.94 million kilometers)”
That’s about 13 times the earth-moon distance.
1986 Halley's comet was closer to Earth then Venus is close to Earth whenever Venus is on the other side of the Sun from Earth
.42AU is a larger distance than the closest that Earth and Venus ever get to each other (i.e. closest than as close as it is possible for Venus to be, with the word "can" being used in this meaning)