Saw this GameFAQs explanation, and it's actually... Good?
"The first three universes have one thing in common: the Lutece Tear. A rip in spacetime made possible by funding from Comstock. The first three outcomes are reliant on an existence of Comstock in order for the tear to be made possible. The tear is the real problem. It is causing the universe to fall apart. It is evident by the tears that exist around Columbia. And the problem is exacerbated as Booker and Elizabeth jump from world to world, resulting in people being caught between dimensions. The very fabric of spacetime is threatened. The only resolution is to eliminate the possibility of the tear. Lutece will always exist. But the funding does not without Comstock.
When Booker drowns, he closes the loop, and eliminates the possibility of Comstock. He rewrites the universal constant. The question is no longer "does Booker accept baptism?" There is no question. Every universe that is influenced by Comstock is eliminated, because there is no Comstock. This leaves only the fourth possibility, where Booker always refuses baptism. He never sells Anna. A new constant, no longer a point of divisiveness in the universe. There is no more tearing, no people caught between dimensions. The universe is fixed. No plot holes, no paradoxes. Everything wrapped up nice and neat."