Instead of corsi, why not just look at the Time of Possession stat?
The value of Corsi is that it is much simpler to track. a Time of Possession stat (NHL doesn't track this currently) would be slightly better, but most research has shown the improved accuracy negligible.
The problem is that may use Corsi as an analogue to something it is not, like defensive play, or quality of player. It's about as useful as +/- in that regard.
Teams don't really need to follow Corsi imo because the are looking for the cause, not a symptom and are willing to spend the resources to comb through the minutia of details. The best thing corsi numbers might do for a team is give them a quick way to narrow down who they want to scout further, but it runs the risk of false positives, and false negatives.
Corsi and other fancy stats are fun for those of us without the resources of NHL scouts, and can potentially be helpful at a strategic level where you can question and evaluate the effectiveness of tactics, but I imagine the teams can do this the traditional way as well (possibly as or more effectively, it's hard to say).
I think what it comes down to is fancy stats can help the layman see what a trained eye already knows. For the untrained eye, it can help help break down biases, and help us question what we "know".