Kelly Hrudey made some interesting comments about broken sticks and penalty killing. Personally I've never seen a player go to the bench for a new stick (or replacement player as seen in the video below), however a compelling argument could be made for taking such action. Not sure at this point how aggressive player's could be at getting a new stick, but certainly players have to at least be thinking about this as an option. In both of the goals you will see below you will notice that without a stick the player is pretty much useless or even worse an impediment to the goalie's vision.
The next day I had a deja vu as I watched a Canucks penalty killers stick break. He tried to stop passes and block shots, but the whole time he was without a stick I couldn't help but remember what Hrudey had said and couldn't help but think: they're going to score.
Now, in terms of penalty killing, leaving your team 5 on 3 for 10-15 seconds to replace a stick, could be killer as it is so easy to score on a 5 on 3: ~24 goals/hour. So a 15 second 5 on 3 is equivalent to about 0.1 goals against (or about 0.075 extra goals over regular PP). Of course the question I cannot answer is how often teams score when their opponent has a broken stick.
Finally, it was never brought up, but why don't these players have unbreakable sticks just for killing penalties? It's not like these players need a stick that can shoot the puck really well