I think it's more that faceoffs can situationally have an outsized effect on the final score.
For example, tied game in the 1st, you get the first powerplay. You win it cleanly and set it up in their zone probably increases the chance of scoring on that powerplay by as much as 20%. First goal of the game is massive. Conversely, if you have a kill, say in the 3rd, and you're nursing a one goal lead, getting possession in your zone and teeing it to the other end is a huge momentum builder to start that important PK. The opening faceoff to a period is usually a lot less important, unless that faceoff is for 3v3 overtime.