Is it critical that every game with a story try and create a First-Person Character Arc? Of course not.
It does, however, represent one of the forward edges of Emotioneering. The rewards for succeeding in making a First-Person Character Arc work are great, but the risks for failing can be serious. You could create a Character Arc that the player doesn't go along with in his or her heart. If that's the case, the player will feel emotionally distanced from the game instead of feeling more involved.
But, if you want to be part of the cutting edge of game design, step right up and take your best shot.