But doesn't travel between the multiverses cause rapid aging? There's no way that Elizabeth could sort out all other possible Comstocks before her inevitable death.
One possible theory is that if Liz can really see "all of the doors", or all probabilities through tears as mentioned by the female Lutece, then somewhere among infinite possible solutions, there is some answer that will absolutely stop all probability of something ever happening that can be obtained instantly.
Also, aging/cancer only appears to happen due to exposure of radiation from the tear machine. If Liz can produce them on her own, it is possible that she's not equally affected.
Moreover though how could she destroy the Comstock that exists in her own personal timeline, without erasing herself from existence? Even assuming that she is immune to the aging effects of interdimensional travel, that Comstock that created her would have to continue to exist.
She destroys all Comstocks at once, including the one that directly created her. As do all of the other Elizabeths created, as seen in the ending where another Booker and Liz are also making their way through the series of lighthouses.
This then creates the paradox of Comstock never existing, and thus, the universe 'rights' itself to only leave Bookers who could never become Comstock.
Like you and I both stated earlier, Ken is purposely limiting the nature of the multiverse around Booker's story at a specific moment in time to create his narrative to try and circumvent the truly 'infinite' nature of the multiverse. Booker's journey is still linear, because it has an end.
