I think a player can be either more finesse or more physical (or, both), but I don't think you can have an identity as finesse only. Physicality is part of football, and it is anchored in the line play. Run first, or pass first, it has to be there. I would rather our identity lie in being unpredictable, or flexible. Harder to game-plan against that.
But to your point of having more of a running identity, I think we will run the ball better for various reasons. But what will make it really click is the ability to throw the ball as well. I'd love to see us run for 2-250 yds/g and throw for 2-250 yds/g on average. But that means some games it's 300-350/100-150 in favor of whatever is working better that day. (I know, I might be dreaming with some of those total yards numbers...).