just because it made it easier for me to reason about the fact that since the sun has some actual width it's exactly equivalent to a body that would orbit at that distance. If you frame it that way then it's rather obvious that the sun also fits the bill as the "mostest closest body" (albeit not planet)
it's not intuitively clear to me whether that is on average closer to the earth or if it's on average exactly as far as something orbiting around that center.
Furthermore, since the sun is also orbiting around the shared center of mass of the whole solar system, this displacement albeit very small, is still enough for me to not intuitively understand if it makes the sun's center of mass closer or farther away on average than the closest orbiting body to the sun
