The discussion around BioShock Infinite's combat doesn't just involve the question of whether its quantity of violence is essential to the story (yes), or whether telling a story where its quantity of violence is essential is interesting or worthwhile (no). Some of the discussion has centered around the question of whether the combat mechanics are any good. Eric Schwarz has written a fantastic post that describes most of the combat mechanics, and I want to expand on it a little. Even though I think violence helps to express the kind of character Booker is, I don't think the combat systems of BioShock Infinite do much to help characterize him, and in some ways actively oppose that characterization.

BioShock Infinite is a violent game, and it has to be. That's a contrast to BioShock, an equally violent game where combat conveyed nothing about its main character and had little to do with the game's themes other than spurring the player to engage in its various economies. Any stimulus—using plasmids to solve environmental puzzles, for instance—would have sufficed. That's not so in Columbia. Violence is essential to who Booker DeWitt is, and what Columbia is. Their story cannot be told without it.