Does the ending actually make sense?

There are a few things about BioShock Infinite that still puzzle me. Most of all, though, I don't understand this:

If Comstock was eliminated from the equation, and every possible reality in which Booker becomes Comstock ceases to exist... then how in the hell did the events of the game unfold? This is a problem I have with time travel stories as well. If you go back and change the past, then that changes the future. If Colombia never existed, Comstock never existed, Elizabeth never had those powers, then the events of the game couldn't have possibly taken place, right? Which means Elizabeth could have never taken Booker back to that moment in order to change the past, WHICH MEANS that nothing actually changes at all. Or am I totally off here?

Was Elizabeth just trying to give Booker some hope? An false sense that he would be able to start over even though she knew "the circle cannot be unbroken"? She can evidently see all outcomes, so she must know something. She says it herself that Booker will always give over Anna (which was another cleaver "commenting on video games" moment like in the original BioShock, as that was literally the only thing you could do to progress) so maybe that's actually a constant. Somewhere something doesn't add up for me. It seems to me that, no matter how many minor variations there are, it's going to lead to the same outcome in all realities.

Also, I don't see why Comstock went through all the trouble he went through to keep Elizabeth's powers in check. Couldn't he just have retrieved her finger? Surely there's a reality where her pinkie is reattached, or at least reunited with her so that she exists in one place. And there must be a reality where her finger never came off at all and Comstock was completely successful. The finger's got to be another constant.

BUT, my understanding is that, to eliminate Comstock, Booker must die before he is given the choice to become Comstock. By this calculation, the baptism scene must have been before Anna was born because, in the reality where he refuses, Anna/Elizabeth exists. If he dies at that point, then Anna is never born which means Elizabeth never exists to set in motion the events that leads him to being drowned before she can be born. Is this a legitimate plot hole or am I wrong in my thinking?

The very last moment after the credits puzzles me, however. It seems to suggest that things have been "reset" back to a moment before he originally gave up Elizabeth. Assuming that any realities with Comstock are eliminated (how in the hell that is managed with Booker still living at the time of Anna's birth is beyond me), a whole new set of realities is created in its place where Columbia never happens. So either it's a happy ending where Booker gets to keep Anna and Lutece never comes to him because that reality never existed (which, by my reasoning, is impossible), OR we're simply back to the moment where Booker is regretting what he's done. Importantly, I think, he opens that final door with his left hand, meaning we can't be sure if his right hand is marked or not. I, personally, think it is.

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