The ending makes perfect sense -- it's just been a matter of us all trying to explain it, in a clear and thorough way.
I'd put it like this:
Liz could manipulate time-space because part of her (the tip of her pinky finger) was in one universe, while the rest of her was in another. It's like she's standing on the border between worlds, one foot on each side, able to see both sides.
To try and regulate this power, the siphon was created inside Monument Island, as a way to restrain her. Liz describes it as a "leash." Once the siphon is destroyed at the end of the game, she's "off the leash," and her power reaches its full potential. She can now see all of the infinite sets of timelines in the universe... including all of the ones in which Booker becomes Comstock.
To prevent Comstock from ever happening, Liz has to create a PARADOX, because the universe "does not like its peas mixed with its porridge," as Lutece put it -- or in other words, nature will correct any paradoxes by obliterating paradoxical timelines from existence.
So, Liz creates a paradox: She drowns Booker before his baptism. This creates a paradox because if Booker is dead, Booker can never become Comstock, and if Booker can never become Comstock, Comstock can never steal Liz, and if Liz is never stolen, Liz never receives her ability to traverse time-space and kill Booker in the first place.
The universe sees this and goes, "PARADOX!" And then obliterates each and every timeline where Booker becomes Comstock.
All that remains, are the timelines where Booker rejects baptism. What was once a "variable" -- an element that can change, in this case to accept or reject baptism -- is now a "constant," like the coin that always comes up heads when the Lutece twins meet Booker again at the Raffle Fair and ask him to flip the coin.
That's an important concept to understand. There are constants -- elements that always work out the same across all timelines -- and variables, or things that are different depending on the timeline. Elizabeth, by creating a paradox, forced the universe to take the "variable" of accepting/rejecting baptism, and turn it into the "constant" of rejection.
And so Booker, while still in debt, will be able to see his daughter grow up. And hopefully things will work out for the best.
Just wanted to thank you for this post specifically. I read the OP and almost this whole thread but this post summarizes everything really well.
I guess my point of confusion when thinking about the multiple universe stuff is that the game never really gets into the nitty gritty of laying down the rules with the paradox aspect or the rules governing why something must be a constant versus a variable. Or maybe it does and I missed it or was too dumb to piece it together.
I basically pieced together the ending in a rough form so the last twist that Comstock was alternate reality Booker wasn't as impactful as I'd have thought. I was loving the ending with the lighthouse stuff and Rapture and seeing that Anna = Elizabeth but I feel like something else was missing. Maybe a better explanation of the constants/variable and paradox aspect? Not sure.
I guess my question is why is the baptism necessarily THE constant that sets everything in motion? Sure, that "makes" Comstock but that would presumably only make him super religous. To me, the big event that would take Comstock from a influential preacher to Big Bad Evil Columbia Prophet Comstock is his meeting Lutece. Is his meeting Lutece and looking through the tears for his "visions" a constant or variable? And why? Why not have an alternate timeline where Comstock exists as just some normal preacher who never met Lutece and thus no Columbia?
Furthermore, on a basic level it seems odd that a hyper religious guy like Comstock would even meet up and get acquainted with a hyper scientific, physicist like Lutece. That just seems like an incredibly odd pairing. How did that come about in the first place? Science and religion don't usually mix well like that. The science stuff made more sense in Bioshock 1 where you had Rapture and Ryan letting science run amok basically. In Infinite, that pairing science with religion seems kind of odd.
The whole thing is pretty sad when you think about it. I admit I was expecting a happier ending, Liz and Booker really grew on me so I find the whole thing kinda depressing, it's a really tragic story.
Yeah, maybe that's why I was kind of bummed out about the ending too. Its a bit of a downer.
Although, in the after credits scene does that version of Dewitt have memories of what just happened? The way he calls to Anna makes it seem like he just woke up or something and is knowingly going in to check on her, knowing the whole adventure he just had. Like the end of Inception with the spinning top, I guess.
Also what was the deal with the very end with your version of Elizabeth? The various versions you see that drown Booker are not the one you had been travelling with, right? Because none of them had the necklace that you chose? So did that version of Elizabeth cease to exist when you passed through the lighthouse door?
Other random thought: I really liked the alternate timelines when they were pretty obvious. Things like having Booker be a Vox Populi martyr and seeing how the world ended up in that state. Or seeing Comstock House and Columbia in a timeline where Elizabeth becomes Old Elizabeth and destroys NY. It reminded me Its a Wonderful Life, basically. But I really liked seeing those very obvious and tangible alternate realities. I wouldn't even mind if more of the DLC were just more stories in those alternate timelines. For me at least, I feel like the game got kind of muddled and convoluted when it wasn't clear when you were jumping through the tears or they hadn't really explained those nitty gritty mechanics of interacting with the various timelines enough.
Maybe explaining some of the mechanics of the timeline stuff or Lutece's research in the course of the game would have made the ending a little smoother and less of an info dump. Like find a kinetoscope or film of Lutece giving a lecture on the timelines and things in her lab or something.