I would never argue that winning any puck battle is useless, and faceoffs are a puck battle. I just think that by using them as a stat, you are diminishing the importance of many, many, many other puck battles, races, takeaways, giveaways, etc that happen on a shift.
Your obsession with turning hockey into into numbers is the fundamental flaw because in reality the only stat that matters is the final score.
There is a reason Billy Bean, Tampa, Kyle Dubas and others create great regular season teams but fail to understand the teams failures in the playoffs. What you and they don't get is the playoffs are a completely different game played by a completely different teams.
Tampa and Calgary last year were a perfect example of how irrelevant regular season stats were in the postseason. Everything changes in the playoffs from the how refs call the games differently to how the players play differently. People often refer to this as the intangibles but in many cases it can be seen.
What you, John Chyka, Billy Bean and a myriad of other that believe in advanced stats don't understand is what it takes to win.
First the rules change transforming the game into something completely different.
To be successful in the playoffs players need to be fearless. And there is no tangible way to measure this. I know it sounds simplistic but it is so much more than that. It is that willingness to without a second thought go down to block a Chara slapshot. It is that ability to not give a second thought if you are winning or losing. It is Stevie Y pulling himself up off the ice with one leg and go into the hard areas time after time and prying himself up off the ice. It requires these players to accept the pain and work through it.
This fearlessness is then used hyper-focus for every little detail and never giving up. The best playoff performers... the legends find ways to do this year after year after year. You can not measure or make sense of this ability and there lies how your complete vision of the Calgary team is indeed a fictional story.