Honestly, these stats kind of are pretty fancy.
For starters, it's an index, which means to apply a holistic score to a variety of data. The validity of an index goes only so far as what goes into it, the equation used to arrive at it, and whether or not those ingredients are properly weighed.
Indexes are easier to do in baseball (where WAR originated) because we can easily weigh baseball plays based on the number of bases received. For example, a homerun is objectively more valuable than a triple. What deserves to be weighed more, let's say, on a goal? The defensive play that got you the puck? The transition pass? The zone entry? The assist? The shot itself? The screen (if any)? Nobody knows.
Baseball also has a level of independence as a non-passing sport that hockey does not. It's a team sport, and you certainly rely on teammates, but you can still accrue results as an individual. If a guy hits a homerun, he would have hit that homerun whether it was part of a 10-run rally, or if his teammates are dead. A homerun is a homerun. On the other hand, a goal is not a goal. A goal is a shot, a pass, an entry, a check, a cycle, a transition, a defensive play, a save, a penalty.
People often argue that hockey has more variables. I don't think that's it. Hockey plays are simply harder to weigh into an index than baseball plays.
In short, WAR is nice in hockey and I think there's some merit to it, but it doesn't lend itself to being an index sport. It lends itself to being a sport where you look at many different sets of data.
And yes, it's fancy.
