so, Kyle Dubas, frequent speaker at analytics conferences, and the organization that made him one of the youngest GM's in the league supplanting one of the most seasoned and another good internal candidate do not believe in analytics?
you do present some good arguments...
I agree that it has to line up with what you see, but I think we need to stop calling things like Corsi and Fenwick "advanced stats" too. They're part of the landscape now and they measure things that are actually happening, they're not voodoo and they are tangible. If you believe in things like goals, assists, shots, scoring chances, you should believe in at least the set of metrics that measure things that happen on the ice. Keep in mind they measure correlation, not causation as well - this is a measurement of what's happening while the guy is on the ice (and compares it to what happens to the same for his team mates when he's not in the "relative" versions), it doesn't state the this guy is the reason why those are happening. Over a large enough sample it becomes more and more likely that the subject player has the effect that the numbers indicate though
when it gets to things that are a little more predictive by nature, like expected goals, I can understand there being a little more faith required