Kyrie seems to want to be the alpha dog of his own team, and appears to define that as having the ball in his hands at the key points of most, if not all possessions, and given that he has not shown himself be elite as a distributor and creator of offense for his teammates, is a recipe for being the perennial leading scorer on a bad team. The Spurs are probably the best run franchise in the league (and I say that not as a Spurs fan, but as a jealous Knicks fan), and part of that success has been shunning players who make and act on such statements of ego, on and off the court, and either benching them into submission or cutting ties.
Kyrie appears to want to to be a prima donna, and as long as Kawai Leonard is in San Antonio, he’ll still be the supporting actor, the wing man, if he went there. Unless Kyrie believes that his move to San Antonio would be in a straight up trade for Kawai.
Kyrie, in my view, is at his best seeking his own shot off of iso’s and that is not Spurs basketball. Now that said, Pop is great at changing his system on offense to get the most out of his players (that skill is what, in my opinion, makes him one of the best, if not the best NBA coach of all time), so I suppose Pop can make Kyrie’s offensive skill set fit in. However, Kyrie very, very rarely puts the effort in on defense and Pop has a history of benching such players, be they role players or part of his big three (Pop has, on multiple occasions benched Tony Parker when he wasn’t happy with Parker’s effort).