The basic wrong assumption being made is that quantum superposition by default equals multiplicity - that because the wavefunction in the double-slit experiment has two branches, one for each slit, there must be two of something there - and that a single-world interpretation has to add an extra postulate to this picture, such as a collapse process which removes one branch. But superposition-as-multiplicity really is just another hypothesis. When you use ordinary probabilities, you are not rationally obligated to believe that every outcome exists somewhere; and an electron wavefunction really may be describing a single object in a single state, rather than a multiplicity of them.

Another wrinkle that is too often overlooked is that superposition is observer dependent.