I think if you fully taboo the concepts of "personal identity" and "existence", the argument evaporates. Before tabooing, your argument looks like this:

1. Alternate universes, containing persons psychologically continuous with me, exist.
2. Persons psychologically continuous with me are me.
3. Therefore I am immortal.
4. Therefore I should anticipate never dying.
5. Therefore I should make plans that rely on never dying.

On the face of it, it seems sound. But after tabooing, we're left with something like:

1. Our best, most parsimonious models of reality refer to unseen alternate universes and unseen persons psychologically continuous with each other.
2. In such models, alternate futures of a person-moment have no principled way of distinguishing one of themselves as "real".
3. Therefore, our models of reality refer to arbitrarily long-lived versions of each person.
   ...
4. Therefore I have reason to anticipate never dying.
5. Therefore I have reason to act as if I will never die.

Edit: My #4 and #5 were nonsense.