I'm working on a longer piece about BioShock Infinite at the moment, but first, I wanted to take a moment to summarize a number of things I've read about it, and throw in my two cents, because it's unlikely it'll fit anywhere else. (It's also more or less spoiler-free.)
Why did it have to be a first-person shooter?
It didn't. Genre and milieu can operate fairly independently of each other in game design. There are, no doubt, some aspects of the narrative that would have worked better in a different genre; there are others that wouldn't have worked as well. The story told in BioShock Infinite is not, itself, BioShock Infinite. But fundamentally, the narrative component--which people seem to be employing as synonymous with the game as a whole--was realized in the first-person shooter genre for the same reason that the earlier Contra Galt story did: because Irrational was designing a first-person shooter when Ken Levine and his minions worked out the details of the story. Genre preceded story here, as usually happens. The disconnect is more obvious when the audience gives a shit about the story, but it's always there.
Why did it have to be so violent?
Primarily because it's a first-person shooter. That said, even if the Columbiad had been a graphic adventure, it would have been pretty violent. Horrific, brutal violence is a constitutive element. Yeah, that skyhook-to-the-face is gratuitous, even by genre standards, and it comes up awfully quick. But this is a story about slavery and genocide, and how brutality doesn't become less brutal because of social agreements not to notice it.
Elizabeth is a lot of fun, and could probably have made any genre or milieu quite entertaining. Maybe we'll get them someday. But this particular story was written for this particular genre, with this particular level of senseless brutality. It would be nice if it could have been something that wouldn't put off non-gamers, and it would have been nice if it had been something that wouldn't alienate people who hate FPSs. Either of those would have been good games, but neither would have been the story Irrational wrote, or the game they built. There seems to be an idea that Infinite is so good that it has a responsibility to grow the medium, to transcend its childish genre, to shun the aesthetic sensibilities of teenage boys, and to eschew any more violence than is strictly necessary. In short, there seems to be a sense that BioShock Infinite is just plain too good to be a videogame.
It's a masterpiece, mind you. It is also a videogame. That's ok.
Meanwhile, for the designers, artists, coders, testers, actors, and musicians involved in the production, it has to feel pretty good to have made a game so impressive that people who were disappointed in it seem to feel personally affronted that you didn't make it with their tastes in mind.