Isn't the Booker you play from a parallel timeline?
My opinion on the plot can be summarized by Bruce Willis here.
0:14
But the short version is that Booker and Comstock are two people from parallel timelines that broke off from the same event: Booker getting baptized or not at a fundamentalist religious sect's revival. Prior to the event, Booker was a Metis scout for the US Calvary and participated in Wounded Knee--murdering lots and lots of innocent women and children in hopes of impressing his white associates.
The Booker who was baptized believed he was cleansed by Jesus and could do no wrong so he went on to found Columbia based on the racist classicist beliefs he tried to follow while a member of the US calvary. He took the name Comstock to go along with being reborn. Eventually, Comstock funded Rosalind Lutece who developed universe-jumping technology (who eventually met her alternate self who was a man).
The Booker who refused baptism went on to join the Pinkertons, became a drunk, and then sold Elizabeth as a baby to a universe-hopping Comstock. However, Elizabeth gets her pinky cut off in the portal and this gives her vast cosmic powers because....reasons.
Elizabeth's power inspires Comstock to believe she's the messiah and he plans to use her to wipe out all sinners on Earth as only Columbia is saved by God. It will take awhile for her power to grow and Comstock puts her in an inhibitor so he can keep her under control until she's an adult. To that end, he keeps her in a tower and studies her scientifically until he kills Rosalind and Robert Lutece in order to make sure they can't stop his plans for Multiversal genocode.
EXCEPT Rosalind and Robert become immortal quantum ghosts instead because...reasons. So, they go to Booker Dewitt the guy who sold his daughter and recruit him. His memory is fucked up, though, because going through multiple quantum realities makes you crazy and confused. It caused Comstock to become an old man prematurely and makes Booker subceptible to suggestion that he represses his memory of selling Elizabeth and is told he's actually kidnapping her to pay off gambling debts.
After going through multiple realities where they find out Booker usually ends up dying and Comstock eventually brainwashes Elizabeth into wiping out Earth, Booker finally corners Comstock and murders him by drowning him in a baptismal font--still unaware he's Comstock's alternate self. Elizabeth's power reaches the point she learns the truth, however, and that Booker and Comstock are one in the same.
Elizabeth believes that as long as a single Comstock exists in any reality, he will corrupt his Elizabeth and use her to wage war on the Multiverse. So, in order for Comstock to die, he must be prevented from ever existing. Booker agrees to murder Comstock in his crib, not yet realizing that he's Comstock until Elizabeth takes him to the baptism and he agrees to die in the past (Elizabeth drowning his past self) that kills all Comstocks everywhere.
But also all Bookers.
Which is stupid and bullshit science fiction.
However, because of it, Columbia never exists, Elizabeth disappears from all realities but one because she's an immortal quantum goddess, and Booker wakes up with his baby daughter.
If you care enough, here's the fifteen minutes of nonsense.