I think you are mostly right.
Sens fan here, just wanting to see the talk, because this is exactly how Karlsson numbers have been the last several years. He was -26 last year, and it was very well deserved.
Now he has been highly passive defensively for some time. Even before the foot injury he was easy to blow by in his own end, last year was even worse. Last year you can almost count 1 goal a game in your net per game which he was somewhat if not fully responsible for, and it was pretty frustrating.
Offensively though, passive is not a usual description for him. Part of it may be learning the players and not trying to be selfish as pointed out, but he was anything but passive with the puck last year, and in my memory never has been. the truth is you need to get him the puck and give him some space. He is so quick and dangerous. Ottawa players seemed to mostly line up for one timers in the offensive zone and let him do his thing. Always seemed to know exactly when to move with the puck, shoot or pass. His instincts are exceptional. I always say a fast player is not just about his skating, but about how fast he thinks the game, and on offense he is one of the best in the league. He makes the best decision lightning quick. He certainly makes up for his defensive deficiencies and then some on offense.
What has his deployment been like? From the first two it looks somewhat correct.He did about 65% offensive zone starts last year (all situations), minimal PK and most of the PP. He did not play against other teams top two lines very much, which made the defensive lapses a bit more painful.