That's how I see it. Stop with the nonsense people. Not every story needs a good ending and I wish that silly post-credits scene wasn;t there to muck up this tale.
I agree as well. The whole tone of the scene is that all Bookers have to die in order to stop Comstock from ever being "created." It really cheapens the entire scene if we're to believe that only "bad" Bookers are killed. He's killed before he can decide; therefore no Booker is supposed to exist after 1890. Therefore every permutation of Elizabeth disappears.
As far as the post credits scene? No idea what that's supposed to be. But I may have just had an epiphany as I typed those words. Here it is, for your consideration:
Let's call the Booker DeWitt you play as "Booker Prime." No idea why he needs to be Prime, it just sounds cool. (Maybe in this reality he's related to Optimus?) Booker Prime is from a universe (or multiverse) where he chooses NOT to be baptized, and doesn't become Comstock. Instead he has Elizabeth/Anna, but then gives her up to Lutece when Comstock comes through to Prime's reality. 20 years go by, right? It's 1912. Booker Prime is then brought into Comstock's multiverse by the Luteces. The year here is actually something like 1930 or 1940, because Comstock is ~20 or 30 years older than Booker Prime.
Booker Prime does all the crap in BS: Infinite, and we get to the endgame. You start slipping through multiverses with Elizabeth/Anna. First time you go to the baptism, you DON'T get baptized. Now, this is where it gets tricky - during this portion of the game you see the baptism from Booker's eyes. According to the "rules" of multiverse travel (i.e. that Booker Prime and Comstock may both exist in a multiverse), you should be seeing through the eyes of Booker Prime whom promptly just appeared in 1890. Instead, you see this baptism (or "not baptism") from the eyes of who we shall call "Booker Not." Booker Not is a version of Booker who chooses not to become baptized. The case could be made that Booker Prime is a future version of Booker Not, and this would be true. In order for any Booker to become Booker Prime, that Booker must choose
not to accept the baptism (and thus become Comstock).
Now that we've got that out of the way, it does little to explain why we see the NOT baptism from Booker Prime's eyes. One could posit that the player simply becomes Booker Not instead of Booker Prime, but I don't believe this since no telegraph is given to player that he is "switching" Bookers, so to say. I've got two theories about how and why you see the NOT baptism from Booker Prime's eyes:
1. You're not really seeing it as it's taken place. When Booker Prime steps through the tear into the 1890 where he doesn't accept the baptism, he relives it. In his mind. In reality, what Booker Prime would REALLY see if he wasn't having a flashback, would be Booker Not refusing a baptism. He'd see himself. But you, the player, through the eyes of Booker Prime, do not see that because he's having a flashback/hallucination/recalling it or whatever.
OR
2. When you, Booker Prime, step through the tear into an 1890 where you don't become Comstock, or see the NOT baptism (as I've taken to calling it), you "become" Booker Not. This makes little sense in terms of the "rules" by which the multiverses function, but does raise an interesting point which I'll come back to in a minute. You "become" Booker Not because Booker Not becomes Booker Prime. Remember, to be Booker Prime, Booker must have not accepted the baptism - otherwise he becomes Comstock. Every Booker who chooses not to accept the baptism is Booker Not. By some whacky-ass rules, Booker Prime replace Booker Not because Booker Not's experiences match Booker Prime's exactly, except for the fact that Booker Not obviously has no experience past 1890.
Now, if we believe #2 to have been the case, there's one glaring flaw: Booker Prime is 40ish years old. Booker Not was 20 or so. That suggests that by the time 1912 comes around, when Booker Prime sets off to Columbia to rescue Elizabeth, Booker would have to be in his 60s.
Roughly the same age as Comstock. Perhaps this somehow explains that it is
actually 1912 in Columbia when Booker Prime gets there, and Comstock is so old because he went back in time (before he went foward?). I'll admit this mechanic makes little sense but perhaps someone else can suss it out.
Now, going back to my #1 theory - where Booker merely "imagines" himself refusing the baptism, or relives it if you will - this would help explain the Booker, or Booker Prime, at the end of the credits. You see, if we accept that Booker Prime wasn't actually being baptised/refusing baptism when he comes back with Elizabeth to 1890, then neither was it Booker Prime who was killed by the Elizabeths/Annas at the very end. Instead, it was some other Booker, and Booker Prime was merely "remembering" it happening - just like the Asian gunsmith guy (name escapes me. Chin Li? Not gonna guess!) "remembers" dying, even though he's alive in this alternate universe.
So when you see Booker drowning in the end, it's not really Booker Prime, the Booker you played the entire game as. Instead, it's some other Booker. Booker Prime is merely "remembering" him/them dying. I don't believe it's every Booker who becomes Comstock - I just think it's every Booker in 1890. So then, the Booker at the end of the credits? That's you, Booker Prime. You never died. Why are you back in 189x with baby Elizabeth/Anna? Who knows. Maybe you took a "door" to then so you could stop yourself from handing her over. That's the ultimate win-win scenario, right? Don't become Comstock, don't give Anna up. So maybe Elizabeth just sends you there. I don't really know.
After writing all this I have a headache. Hopefully it makes sense. Someone else has already probably come to the same conclusions. If you have objections/need me to clarify things lemme know.