Champion status shouldn't reflect rating IMO. They measure different things (your ability to perform in the highest pressure tournaments, versus general skill)
He can change this by continuing to win more and lose less. To reflect being #1 he needs to take #1 from Magnus. That is probably the hardest challenge he will face in his career/life.
What is the problem? That the reigning world champion isn't also the highest rated player (or strongest player when there wasn't a serious rating system)? That has happened many times before, even not counting the PCA-FIDE title split era. Think of Karpov in 1975 when Fischer was in the background like Carlsen is now.
As for Caruana and Nakamura, well, they played in the same Candidates' as Gukesh. They didn't win it and Gukesh did, so what do you want to happen?