Now that Burial At Sea has definitely concluded the Bioshock series, as Irrational Games are downsizing heavily, the puzzle pieces that we're left with doesn't fit one bit.

Spoilers for every Bioshock Infinite ending:

Bioshock Infinite ended wierdly. It was shocking, sure, but there's no reason for Booker to die. He was the one who clearly repented, so if there ever would be a "last Comstock" to murder, it would be him.

Also, Booker wanted to kill Comstock before he even made the choice, to end all Comstocks, but instead Elizabeth just chooses to murder just his version instead. There is absolutely no reason what-so-ever to do this.

Moving on to Burial At Sea Part 1, the last Comstock doesn't get his empire. He just decapitates a baby, and regrets it for the rest of his life. He turns into a man who wants to save little sisters instead, from people like Elizabeth. Again, no reason to kill him either, unless you want to make Elizabeth out to be a bloodthirsty monster who just wants to kill her father over and over.

Elizabeth herself isn't plausible either: He can run the minute she gets out of her tower, pretty unphazed by the world around her. She doesn't stumble around like a caveman, because "she's read books".

During the Infinite series we can see a steady decline of story sense: The ending to Infinite, the story of Burial At Sea Part 1, but it really turns completely senseless in Burial At Sea Part 2.

"I'm dead. I feel smaller. I have my pinky back? Must be quantum entanglement and singularity and ooga booga, and I have Booker in my head, who isn't really Booker!"
The only real explanation that makes sense, is that Elizabeth isn't really Elizabeth, but her consciousness mixing with Bookers consciousness inside the eve of a little sister. Elizabeth wasn't small enough to crawl into the ducts herself in burial At Sea Part 1, but she is in Part 2, and none of the splicers are able to either, or they would all be extict.
...but no, Elizabeth is really a singularity of all Elizabeths.
...and Booker isn't even Fontaine playing along with her delirium - he's just a ghost of senselessness, conjured up by guilt.

You'd expect a world like Bioshock to keep true to harsh reality, but instead we get "thorn in the paw" imprints triumphing over completely sensible sentific solutions: Somehow hugging someone's hand is all it takes for a wierdo bird to keep somebody captured. They do hint that there's a man inside Songbird, which would make him maybe five times as big as a normal man, so it's so clearly not Booker.

Also, Elizabeth is stupid as shit. She knows that Fontaine would keep his end of the bargain, yet she does absolutely nothing to save herself. She's just fixated of saving one single girl for absolutely no reason, doesn't steer the ships anywhere in Columbia when she's free, doesn't trick Fontaine, doesn't fake the note, doesn't use her plasmids, and doesn't make any attempt to run away. She just hands Fontaine a super-weapon, gives up, and wants Fontaine to kill her, because she's a complete and utter moron.

So what else is just made up story as it goes along? The Luteces. They're scattered all over reality, but they don't have any other motive than to want to turn Elizabeth into a killer, just because wednesday.

Why the story doesn't make sense, doesn't make sense, because Irrational Games had the opportunity and the budget to make it make sense. Instead they made a story-heavy game where the story completely self-destructed with ass-pull after ass-pull after ass-pull.