The issue is that the MWI does not address the phenomenon of single path being empirically special (your path). The theories as in the code that you would have when you use Solomonoff induction on your sensory input, have to address this phenomenon - they predict (or guess) sensory input not produce something which merely contains sensory input somewhere in the middle of enormous stream of alternatives. [putting aside for the moment that Solomonoff induction with Turing machine would have troubles with rotational and other symmetries]

That is true of physics in general - it is by design is concerned with predicting our sensory input NOT 'explaining it away' by producing an enormous body of things within which the input can be found, and this is why MWI, the way it is now, is seen as unsatisfactory, and why having the un-physical collapse of CI is acceptable. The goal is to guess the sensory input the best, and thus choice of path - even if made randomly - has to be part of theory.

Furthermore, if one is to seek the shortest 'explanatory' theory which contains you and your input somewhere within it, but doesn't have to include the 'guess where you are' part, the MWI is not the winner, a program that iterates over all theories of physics and simulates them, is - you get other sort of multiverse.

edit: On a more general note, one shouldn't be convinced simply because one can't see a simpler alternative. It's very hard to see alternatives in physics. Here is a good article about the issue.