indexical uncertainty in the space of all worlds leads to subjective randomness. Their presence plays an important role.
What is the probability distribution on the space of all worlds underlying Everett's interpretation? Without an assumed distribution, nothing definite follows.
Even given such a probability distribution, it only leads to subjective randomness in the space of all worlds, not in the single world we observe. To see this, simplify the space of all worlds to be just $[0,1]^n$, with uniform distribution. Then drawing worlds is a stochastic process, but each particular world is completely deterministic.
For $n=10$, say, the world  is just as likely or unlikely as  or  or . One therefore cannot deduce anything probabilistic about a single world from an assumed uncertainty about the space of all worlds.
For more complex worlds we have the same paucity of deductions. Any inference from a probabilistic law to a particular realization is mathematically spurious, hence based on wishful thinking or silent assumptions.