The problem with Bioshock Infinite is the same problem that comes with all Bioshock games; the "game" part is always the least engaging part.
Each Bioshock opens with a memorable, highly cinematic intro sequence, features a few minutes of roaming a non-hostile environment, and then railroads you from one amusement park set-piece to another. The moment weapons are drawn and crazed fanatics start gibbering, the game just becomes comically out-of-place bar brawls and shootouts, desperately being glued together by a lot of System Shock 2 voice recordings, and the occasional faux-shocking twist revelation or pretentious cutscene blather with a bad-guy.
The reason combat worked in System Shock 2 was that you were in a genuinely dead environment, filled with alien-infested crew and creepy suicide robots that'd wander in while you were exploring (read, while EXPLORING--big factor here) with your back turned. In Bioshocks, the games are always too shoved-up their own story to ever let it sink in that the enemies might be scary--and they're all just 'people' to boot. Sure, some of them are ugly people, but half their dialogue makes them seem like cartoon characters that would seem appropriate walking out of the setting of Team Fortress 2. Even the Big Daddies are threatening in the least direct way possible, and fighting them is something you always do on your own terms. Hell, there's practically an alarm bell any time you have to fight a splicer, what with them giving themselves away from a mile with banal jabber meant to be intimidating. Then you have Burial At Sea part 2, where they're so desperate to conjure fear and tension into the game that they have Sander Cohen make a "LOOK BEHIND YOU" gag to try and get you to jump.
I think if the Bioshock crew spent half as much time trying to make a game specifically for its congruous gameplay, as they do hyping up the bloody things cinematic elements, violence wouldn't even be a concern. As it stands, the games don't even make the violence that particularly 'relevant', let alone jarring. By the end of most playthroughs, I'd slaughtered ten times as many people as any of the actual antagonists, and any time I encountered something breathing, my first instinct was to beat the snot out of it just to get it to stop rambling on. Then I had to ask where all the nice people teleported off to, in order to give room for the loonies with the Lady Liberty masks to jump in. Perhaps they all realized at once, that they were in a Bioshock game, and that eventually they would either have to go crazy or be forced to vacate the premises, and having made this realization, willed themselves from being.
Not the stunning orgasmic game-of-the-year experience I'd expect of a game with this much clout, and it's embarrassing that all it takes these days to clinch that title is a modestly good support character who can summon samurai into department stores for whatever reason. What I'm wondering is what would happen if we got more of the juiciness of Burial At Sea Part 1's opening moments--just exploring an interesting location with interesting characters, without it becoming a monkey house of bang-bang and fireballs.