The true situation is that the Schrodinger equation straightforwardly predicts a proliferation of worlds when you start from a low-entropy state. (Worlds in this interpretation are actually continuous blobs of amplitude, not discrete objects, which is why it makes sense that a partial differential equation like the Schrodinger equation can describe them. The prediction is that blobs will tend to spread out, split into smaller blobs, etc.) Early quantum physicists were disturbed by this, and added a collapse postulate claiming that the wave-function will sometimes spontaneously collapse, resulting in a single, linear world history rather than a branching one. To this day, spontaneous collapse has never been observed in an experiment.
The second mistake is that you don't seem to understand Occam's razor - yes, it is a heuristic, to determine which theory to weigh as more likely, due to limited time and scientific resources. Furthermore, the idea behind it is that, all else being equal, including available evidence, you choose the simpler theory.
If you had evidence that differentiated the two, you wouldn't need Occam's razor.