This, and especially this, reminds me of something I did long ago which, it turned out, had already been done by Hepp expanding on von Neumann’s treatment of the measurement problem.
The idea was to explain “collapse” of the superposition into a mixed state on the basis of having the measurement process consist of interaction with a macroscopic apparatus which would typically of course always be prepared in a mixed state itself.
I haven’t really thought how the “many worlds” approach relates to the “mixed state of apparatus” idea, but the latter seems to me more natural and does not seem to require the extra philosophical overhead.