I believe all this personality based stuff is wildly overrated. Good teams keep winning regardless of this stuff; likewise, bad teams keep losing even when all players get along and nobody sulks.
The problems are on the court. Too many players are anxious - desperate for their next shot. So they drift toward playing selfishly.
Notice how often players stay back after putting shots up, or even after made baskets, hunting for opponent's outlets and even inbounds passes after made baskets. Awful for the team, but a chance for glory for each individual player.
Then Kyrie isn't the type of PG that is capable of, say, rewarding a guy who's hustled or defended well or is anxious for a shot. Get a guy who's struggling going. Find a way of creating a good mismatch for that player. Letting someone initiate the offense and just play off-the-ball for a few possessions. He's good at making baskets, and even at creating baskets for others when he focus on that, but not at managing this kind of stuff. And his defensive effort is super uneven. Just a complicated player to have leading a team. To me, this is far, far more important than anything about his personality, if he laughs or sulks or whatever.