Physicality is perhaps overrated as a practical element to one's game, but is underrated as a way to judge a player's mentality. Not talking about pure hitting (ala Douglas Murray) that can set a tone on a game-by-game basis, but your general Cal Clutterbuck-style hitting.
There is a definite stigma attached to players (especially those with size) who don't play physically.
Think about back in the day, players who didn't block shots. It hurt to block a shot, and really, it was a marginal team gain for a big personal sacrifice...the individual takes the pain and risk of an injury in exchange for stopping a mini-scoring chance.
Physicality is the same. Hitting a guy may slightly help in getting the puck from him, but it seriously wears down on the body. Over a career, its going to cost a player billable years. There is always going to be the notion that players who don't want to engage physically are putting the name on the back ahead of the logo on the front.