Craig Custance has a great (unfortunately insider only) piece on coaching salaries in the NHL, and Mike Babcock’s stand for his fellow coach. It’s a very interesting read.
The biggest reason why hockey is so in need of a catch-all stat isn’t for basic analysis, because combining different metrics isn’t so hard, but it’s so that there’s a baseline for salaries. Being able to say that Bryan Bickell adds 2.4 wins per season above replacement but Joel Quenneville adds 3 would be huge, and would affect salaries in a big way, equivalent to what has happened at the GM level in baseball.