A guy like Erik Karlsson, as you seem to think "always has the puck", his team only has the puck around the 50% mark. And him personally? Probably not far above 10% of the time. It's rare any players have CORSI, which, by the way, includes when ANYONE on the ice with him on his team, has the puck, over 55%.
This idea that if you have a 55% CORSI, it really doesn't matter what you do when you don't have the puck, is so unbelievably short sighted. You can't ignore what a player is doing FORTY FIVE % of the time. That's absurd.
Not to mention, you take possession, and avoid the puck ending up in your own net, mostly due to what you do when you do NOT have the puck.
People who want to ignore what a player does, at best, 45% of the time they are on the ice, because they are doing it 45% of the time, instead of 50% of the time, like other players, are totally out to lunch.
Do you want the player that contributes to his team having the puck more than 50% of the time? Of course. Does that mean you ignore 45% of his play? JFC no. This is one reason why CORSI nuts can't be taken seriously.