I'm on vacation and not in the mood to go on a long rant about Brodeur's unprecendented ability to keep shots against down, so I'll just make a few bullet points.
1) His puck handling ability changed the strategy of entire teams. Dump and chase teams like the Flyers had to adjust their offensive strategy, because they knew that any soft dump was coming right out.
2) Brodeur's ability to move the puck out of his zone by himself meant less wear and tear on his defensemen, is a big reason why they were rarely injured, and thus contributed to the strength of the defense in front of him.
From 94-03, Stevens missed 18 games total.
From 94-00 and 01-04 (removing his holdout), Niedermayer missed 38 games total.
The fact that Brodeur's puckhandling completely negated the soft dump in meant his dmen didn't have to take punishment in the corners, which made them less prone to injuries, which in turn made the defense in front of Brodeur better.
3) The negation of the soft dump in made Brodeur's defensemen able to hold the blue line with much more confidence.
4) The NHL changed the rules because they thought Brodeur's puckhandling was so good, that it was breaking the game! Yes, they never specifically said the trapezoid was because of Brodeur specifically, but everyone knows that if it wasn't for his tremendous success as a 3rd defenseman, they would have never made the rule. Without Brodeur's dominance, the puck moving ability of guys like Turco and Dipietro would be more of an interesting novelty.
The rule was Bobby Clarke's brainchild, and Clarke had been complaining about the way Brodeur negated dump ins for years. (Note point 1 again on the especially large effect Brodeur had on dump and chase teams like the Flyers). I know some around here try to diminish the effect of Brodeur's puck handling, but if it wasn't important, why would the NHL create a new rule to stop it? Gretzky is the only other individual player I can think of who "broke" the game so much that the NHL had to change the rules to stop him from doing so (the end of 4 on 4 for coincidental minors). They did it for the 50s Canadien powerplay, but that was a group of players.
Google "Brodeur Rule" for various links if you want support.
5) Relatedly, Brodeur is very aggressive with the pokecheck, which stops shots before they register on goal. Very different from a butterfly goalie who would tend to let the shots hit him, thus counting as a save.
