So he needs good coaching
I think it's a lot more than that. I don't know how elite athletes prepare, both mentally and physically, but quite certainly they have very specific plans designed by very smart people to help them stay elite in their domain. Such a change, including potential new coach, changes the entire dynamics. I'm sure they are hesitant to make such changes, that could impact their core strengths without equivalent compensatory improvement in other areas.
Yes, elite players do add to their game even at later stages, and there are many instances of players improving their free throw or 3 point/outside shooting to add to their core skills. I don't know how many players with questionable defense have significantly improved their defense. Perhaps this is not so easily measurable, so doesn't stand out, but I don't recall reading a lot of such new items.