As for the case of CP3, not the first time, we have seen a lot of great players not winning a ring, like Charles Barkley and yet they are still in the discussion as great players. Perhaps the closest that CP3 could have won is with the Rockets, but he got injured and so they lost that series against the Warriors and then the Dubs winning that champion that year. They still have a chance next year, but it was a disaster for them.
The fact that Paul signed a one-season contract with the Spurs this offseason indicates that he has probably decided to give up trying to get at least one ring. Obviously, he won't be able to do that with Spurs in the upcoming season. Besides, he will be 40 years old next year, so I wouldn't rule out that the upcoming season could be the last of his career.