I don't understand why you don't think this rule is necessary. We saw exactly why--because if you are wearing tape on your hands and you punch someone, it can cut them, which is exactly what happened. Most players aren't so unsportsmanlike to tape their hands with the intention of using it to their advantage in a fight, but the rule is there (1) so that if a player does have tape on their hands for injuries, they don't fight in that game because it isn't worth the match penalty if the other player is cut or injured because of it, and (2) because there are still scumbags like Zac Rinaldo in the league so you need to have rules to prevent people from doing something like this on purpose.
The additional penalty for instigating a fight while wearing a visor is no longer in the rulebook. They obviously took that rule out when they made visors mandatory. Kalinin was not given a match penalty because Miller was not cut or injured. "Any player wearing tape or any other material on his hands (below the wrist) who cuts or injures an opponent during an altercation will receive a match penalty..." Again, the rulebook is right there on NHL.com, there is no reason for anyone to be confused about this.
You almost never see this penalty called because it almost never happens. I am very confident that this rule is enforced every time it is supposed to be, that is why you never see fighters wearing anything on their hands even though their hands take more abuse than any other player. Miller and Kalinin aren't fighters, so they probably never gave it much thought.
So Miller was penalized for winning the fight?? Nothing weird about that. We'll just have to disagree.