^ score effects simply try to explain the anomaly. If outshooting wins games then total shots would result in more goals regardless of what time of the game they were taken.
What happens is that talent (ie conversion and goaltending) erase any impact these metrics have.
If Corsi is a .30 correlation that means that of 10 teams only 3 would demonstrate results you would expect (ie possession, shots etc leading to wins or lack of leading to losses). 7 wouldn't.
If you look at correlation coefficients, you will find it generally ranges from .3-.4. Meaning 3-4 of 10 teams would show results consistent. A couple may be .5 or even .6 in the rare case. Which of course means half the league has results opposite to what you expect (ie bad possession and actually win or good possession and lose... like the leafs).
So how about the correlation between the teams in the final 4 right now or previous cup winners? Out of the 3/4 teams you suggest (I wouldn't disagree with that logic, expand to 9-12) how many of them are in the final 4? How many of those teams won in their respective years?
I honestly don't know but I would expect a r value increases closer to .6-.7.
I think again this is when you have to look at each team and explain why they performed how they did.
Regardless of the stats, can we agree that teams should aim to be strong possession teams who win more games?
So now why did the Leafs have a higher Corsi but finish dead last? Was talent the issue? Was PDO the issue?
I'd first look at our PDO. We finishes dead last in the league. We had .904 goaltending. That isn't good enough and we lack talent in the goaltending department (we all acknowledge). How about our shooting percentage? We had a .076 shooting percentage. That also isn't good enough and we didn't have the talent on the roster to score goals (we all acknowledge this).
So now we know the goaltending wasn't good enough and the scoring wasn't good enough BUT we did generate shots and in general we out chancing our opponents. Our coach did his job.
Whats next? Well we know that our coach is going to promote a style that leads to more chances for us and less against. Let's put the talent in the system now. Now we have talented players who are creating more chances while giving up less and a goaltender who is saving more pucks on less chances.
Do you see my POV now of looking at it with a little more context?