possession time is important because the other team can't score when they don't have the puck. i.e goal prevention.
i think with certain top tier players like Pat Kane as the most glaring example, he can simply hold onto pucks and make plays that most other players can't make instead of just hurling the puck to the net.
Kane's shot metrics aren't very appealing and the "eye test" says he is one of the best individual possession players in the league.
If the end result is goal preventation, a high shot volume- average time of possession team can still end up with same results as mid shot volume- high time of possession team but being able to keep a team to outside even tho they have possession
We do already measure that end result of goals and shots. Time of possession only muddies the waters more because that stat by itself is not at end, only a means to an end. Shots are still the end.
For example, 1 team can possess puck 70% of the game but only get 45% of the shots. They are largely just being ineffective with the puck. But would people start saying "oh well that team is a better possession team because of time of possession"
Time of possession would be a good micro-stat like zone exits or entries are. They are good for looking at smaller, select aspects of a game. But time of possession wouldn't and shouldnt replace shot metrics as the larger all-encompassing metric to evaluate games and players. Because the end result is still to get shots on net and prevent them on yours
As for your example, its actually pretty good. Pat Kane has poor shots for (145th overall for forwards) and shots against (155th overall). He does however rank high in individual shots for (7th in league for forwards). So I get where your coming from, but its a bit off because Kane does shoot it a ton, its his line that doesnt shoot (next forward has 40 less shots on his team). The question is: is being on a line with low volume shooters costing him and the team more than its benefiting them? His goals for% is below average on the Hawks. Would shooting more get more goals for him, his line and his team. And if shooting more meant losing possession and hsots against, does good outweigh bad
Basically, even right now if Kane is a monster at time of possession, the result of goals scored and goals scored against isnt doing Kane all that well. Would lowering T.O.P and increasing shots do them better?