The thing that makes Chris Paul good is also his biggest flaw and that is Chris Paul led teams rely on him to carry an extremely heavy load on both sides of the floor. No player in the history of the NBA has been able to succeed in the playoffs while having to lead the defence and initiate the offence every time down the court in order for his team to be successful.
Of course you can make the argument that Chris Paul's ball dominance doesn't allow his teammates to learn how to initiate offence without him but the reality is that the best players he has played with are David West, a pretty good player who was an all-star mainly because of CP3 getting him open in the mid-range off pick and rolls and Blake Griffin, a great player that seems to consistently shrink in 4th quarters.
I think the Chris Paul narrative would have been a lot different if he had a more reliable second option he could rely on in the playoffs at some point in his career. People forget that CP3 was well on his way to winning an MVP with the Hornets the year he fukked up his knee, and that was in a league with many legendary players (Lebron, Wade, Dirk, Kobe, etc.) still in their prime. I mean the guy is really good but he's had to do too much for his teams throughout his career.
All that being said, Chris Paul has never been clutch in the playoffs either. Too man key turnovers and bad offensive decisions in key moments. He's a tremendous player but I think he has a mental block in regard to believing how good he actually is, which is why I think he freezes in big moments. And now, with his age, I think his window has closed as a first option.