Does it make sense to normalize?
First, let's look at the term normalization.


  In statistics and applications of statistics, normalization can have a range of meanings. In the simplest cases, normalization of ratings means adjusting values measured on different scales to a notionally common scale, often prior to averaging. In more complicated cases, normalization may refer to more sophisticated adjustments where the intention is to bring the entire probability distributions of adjusted values into alignment.


Your NHL goals example probably does not need "adjusting values measured on different scales to a notionally common scale." 

Think of the handful of players who had a high-scoring beginning of the season, and then was injured and sat out the majority of games. Would you want to normalize his goals up proportionally to the rest of the league?