Sorry if this adds to a pile of threads complaining about the ending. Let me preface this by saying I love the first Bioshock and I really enjoyed this game up until the ending which left me in a kind of dazed funk (but not in a good way). But I feel it will be good to get this off my chest. Warning: long post.
1. The ending dazzles you with talk about infinite branching realities, but then goes on to ignore the most basic paradox of time travel--that changing the past would alter the future in a way that would not lead to you going back to change the past. The way that time travel is generally seen as possible (at least in sci fi) is that travel back to alternate pasts is possible--thereby creating a new branching timeline. This fits with the general series of events in the game. However if that held true for the ending, the Elizabeths would have killed Booker/Comstock and created a new timeline where Comstock did not arise--but they would have remained. They would not/could not have eliminated him in a way that would have prevented their own existence.
I saw no mechanism in any of the discussions in the game for how Elizabeth(s) could have transcended this paradox. And it really flies in the face of there being infinite variations of this scenario.
2. Having played it all the way through, the game really boils down to a narrative of child abuse. When you first encounter Elizabeth, she has been held in near solitary confinement for years by Comstock. You rescue her and lead her through multiple violent encounters while you lie to her about your motives (which is essentially human trafficking).♥♥♥♥♥♥happens, you grow closer to her and try to help--but then she is taken away and subjected to a lifetime of torture and brainwashing until you encounter her as an old woman, razing 1980s New York city with....zeppelins. But she sends you back in time to right things.
After rescuing young Elizabeth, you are not allowed to take her to Paris. When she asks you if "you really want to go through with this" the player is given no choice in the matter. Then Booker/Comstock is drowned and all the Elizabeths cease to exist. So the character you play is killed and the emotional driver of the storyline ceases to ever have existed. Imagine a great novel where, at the end, an omniscient narrator appears and says "oh, actually none of the events you read actually happened. The hopes and aspirations of the characters don't go anywhere because it turns out that none of them actually lived."
At some point, the developers got so enamoured with the idea of variables and constraints that they discarded the significance of the characters as moral agents and the pleasure the player feels for making a difference within the confines of the game world. Imagine in Bioshock if you had spared all the little sisters and then at the end they all drowned anyways, regardless of any actions you may have taken to save them. If I play this game again, I'm going to feel like a real prick when I interrupt Elizabeth's dance on the beach since that's one of the few moments of genuine happiness the character experiences.
But wait--there's the Schrodinger's baby cutscene after the credits. Possibly a reality where Booker doesn't give away Anna (who still would never become Elizabeth). Given that the child is actually there--YAY! WE ARE BACK TO SQUARE ONE. There is an infant in the hands of a morally compromised, debt-ridden, alcoholic single father. The is no reason to believe that Booker would somehow remember the events of the game narrative, which never actually occured. So it's entirely possible that he'll sell her off to the first pedophile that comes knocking. Or he'll drink himself to death, or whatever.
Bioshock Infinite is like a Greek tragedy where good people fall into ruin do to a chain of events that they don't understand and can't control. Except the story has no good people, only victims.