Can you imagine if soccer or basketball, or other similar sports removing a player from the playing area for committing a foul?
Imagine if they gave both teams a 50/50 chance at the ball everytime the ball goes out of play?
Some of the rules of hockey just don't make sense. Currently, there is only one way to restart play after a stoppage - face-off. Doesn't matter who causes a stoppage, both teams have an equal opportunity to regain possession.
So, what is an alternative? Well, face-offs are a part of the games history, so let's work with that framework.
Free Face-off - teams line up for the face-off, but only one team is able to play the puck. Teams can create set plays for an instant scoring chance.
A Free Face-off would follow any stoppage caused by one team, in the zone where a regular face-off would occur. Examples: Icing, puck over glass, offside, contact with high stick, hand pass, etc.
It would also replace most minor penalties (tripping, hooking, interference, etc). Instead of a powerplay, offending player still spends time in the box, have a Free Face-off in the offensive zone. Instant scoring chance, and then play on 5 v 5.
Similar to basketball, after a certain number of fouls, or for serious fouls, powerplays could be awarded.
Hopefully, this lesser penalty will encourage referees to call the rule book more closely.