It has been argued the exponential size of the wavefunction can be interpreted as many parallel worlds, and this explains how quantum computers can factor large integers and compute discrete logarithms (although on closer examination, Shor's algorithm doesn't work at all by trying out a superposition of all candidate solutions. It works by using number theory to find a different function with periodicity, and period finding.).
However, unless we can examine specific individual branches of our choice, why should we argue for the ontological reality of the branches? Measuring which branch we are in "collapses", i.e. picks out a branch sampled at random, and not a branch of our choice.
To be more specific, let's say we wish to invert a one-way function f with no periodicity properties, i.e. solve $f(x)=y$ for a specific y. We can easily prepare the state $C\sum_x |x\rangle\otimes |f(x)\rangle$ where C is an overall normalization factor. However, unless we can also postselect for the second register being y, how can we interpret this as many parallel worlds?
Doesn't this inability argue for a more "collectivist" interpretation where the individual branches don't have "individual" existence, but only the collective relative phases of all the branches taken together have any real existence?
To take a less quantum computing example, consider Schroedinger's cat. Suppose we have N cats in N boxes, and we perform independent cat experiments on each of them. Let's suppose I pass you a prespecified N bit string in advance, and I ask you to "subjectively" take me to the branch where the life/death status of the cat in the ith box matches the value of the ith bit. That, you can't do unless you perform this experiment over and over again for an order of $2^N$ times.
PS Actually, there might be a way using quantum suicide. Unless the life/death status of each cat matches that of the string, kill me. However, this rests on the dubious assumption that I will still find myself alive after this experiment, which rests upon the dubious assumption of the continuity of consciousness over time, and that it can't ever end subjectively.