To me, the idea of adjusting the size of the nets is met with way more outrage than it should. We're acting like the 4' X 6' is the holiest of holy parameters of hockey, whereas in fact that's not the case at all.
It used to be that hockey nets were just two stakes driven or frozen into the ice, with no crossbar or netting or anything, it looked like goalposts in football. There was a goal judge right on the ice, behind the net, to determine when pucks had gone through. Eventually the crossbar was added, and someone had the bright idea to put in the mesh.
Also, at the time, goalies weren't allowed to drop on the ice to make saves, they had to remain standing. So lots of moving parts, lots of variables in this equation, and big changes during the development of the game.
Just because the dimensions we use now are nice round numbers doesn't mean that they're immutable. Basketball is caught in this trap, and I think suffers from it. The height of the rim in the past, when small players lobbed underhand at it, wasn't a factor, but now with seven-footers and players who can dunk, it does come into play.
Volleyball has a variable height of its net depending on the level of competition and gender. College kids play with a net set lower than Olympians do, and that makes sense. And it's not at arbitrarily 'even' round numbers, but rather numbers that allow the bump-set-spike game to unfold at each level, but not be so achievable that it becomes a farce when too easy.
Hockey nets could easily be made wider by nudging the posts outward a couple of inches each or so. The argument that goalies nowadays are prepped and coached to within an inch of their life and doing so would change their angles and confuse them to me is not a valid counter. Because that's exactly what we want, to move the sport away from systems and coaching, to individual creativity and talent. Carey Price and Roberto Luongo would adapt, and maybe some of the others who are more tall than good wouldn't, and that's where we want to head.
As I've stated before, I'd be leery of making the nets taller, more than a couple inches at most, in fear that doing so would incite players to shoot ever higher. 100 mph slapshots are best kept low. Players shouldn't be rewarded for whizzing shots at the height where others' chins are. Safety considerations should keep the crossbar at this level it is currently.
There was a picture of an oddly-shaped net that circulated during Gary Bettman's Third Lockout that piqued my interest but which I haven't been able to find since then, the posts were the same distance apart as currently at ice level, but then flared out at an angle, before being perfectly vertical again at about the three-foot level. This configuration didn't mess with the goalie's 'angles', but would provide lots and lots of room upstairs for snipers when goalies dropped to their knees.
Another proposed net just kept the same dimensions, except that the posts and crossbar curved, they bulged outwards at their middle, again giving more room for shooters but not changing the goalies' coaching and angles.
Either of these alternatives could be tested in camp 'lab' conditions, in lower leagues, during exhibition seasons, etc. You could see which solution worked, fostered more 'clean' goals, allowed talented players to see more net and find it with the puck, and there's every chance that no one would die.
Baseball has done this in the past too. The pitcher's mound now rests at an odd 60'6" distance from home plate, but it wasn't always that way. It used to be at a 'round' number in the Abner Doubleday era, but was adjusted closer or farther based on how hitters were faring hitting the ball, among other changes baseball made to its game. Same with the height of the mound, it could be raised or lowered, and was, based on whether the hitters or pitchers had too much of an advantage.
Goalies used to be, according to lore, the short fat kids who didn't skate well, who couldn't be used elsewhere on the ice. They were wearing the stinky moldy communal rink or league equipment made of leather and felt, or bore the additional cost of their own gear. During the game they were told to adopt a 'standup style', and followed this since, weighed down with so much waterlogged gear, they learned quickly that getting back up after flopping down was very tiring.
Nowadays, goalie is the glamour position with swoosh gear that many kids are drawn to. Tall athletic kids who in the past would play centre now end up in goal. They're armoured with closed-cell foam and kevlar and other space-age materials that are better and lighter than horsehair.
These changes are counterbalanced somewhat by the better composite sticks skaters use nowadays, but not completely. While skaters can fire off better shots at the net, the advances in goaltending have been greater.
So there's no sin in trying to move the needle back a smidge, give goalies a bit more of a challenge.
I completely agree that obstruction and other anti-hockey tactics should be refereed out of the game. Systems should be less important than the talent of a Mario Lemieux or Connor McDavid. Maybe enact 'illegal defences' like the NBA does. Outlaw teams lining up four or five abreast at their own blue line. I've read before a suggestion that forwards shouldn't be allowed to skate backwards in the neutral zone when they're defending.
So sure, first and foremost open up the game, let it flow. Let the players play, let them decide the outcome of the game, but by this I mean the real players, versus checkers and grinders and 'energy' players. I mean the opposite of what Don Cherry means. Generally, in fact.
But in tandem with those approaches, there's nothing scandalous about increasing the size of the net, in a reasonable response to the way the goaltending has advanced since the 4 X 6 was enshrined in the 1920's or whenever. A hundred years of progress in other facets of the game should be reflected in this aspect of the rules as well.