There are two problems, really. The first, as you note, is the league. Bettman and Goodenow are doing an awful job. That's self-evident. The lack of a season would is one clue. The sad tale of the Phoenix Coyotes, NHL-owned since 2009, is another.
Playing anything on ice is expensive—in more ways than one
But let's ignore how badly the league runs, or doesn't, and consider some larger concerns about the game of ice hockey itself. Like you say Jake, the modern fan has options. If people are choosing Aussie Rules football over hockey, it's fair to ask why.
First off, playing anything on ice is expensive—in more ways than one.
Literally, of course, pucks, goals and skates aren't free. Neither is rink time. But the sport also suffers from what I'd call the "Centrifugal Bumble-Puppy Effect" —named for the hyper-complicated pastime of the masses in Aldous Huxley's Brave New World. Hockey involves so many people, so much equipment, and takes such a specialized playing surface that it almost seems designed to consume resources. It comes off as gauche somehow in these carbon footprint-conscious times to watch people ice-skate in Arizona.
Which gets to the game's bigger problem. Winter. People hate it. The population of North America has been steadily migrating into Sun Belt cities for decades. That, plus a climate pattern that seems to be warming suggests that far fewer people will be growing up next to frozen lakes with hockey sticks in hand, which in turn means a lot less people to play or care about the sport.
Overhauling the NHL—including contraction to 16 teams—makes sense in the short term. Half a league is better than none. Generally, though, pro hockey is headed for the dusty shelf labeled "sports your grandfather cared about," where it will sit next to a bowling league trophy, a pair of amateur boxing gloves, and the shoes he wore to play stickball.