I agree that MWI doesn't help much in explaining our sensory strings in a Solomonoff Induction framework, relative to "compute the wave function, sample experiences according to some anthropic rule and weighted by squared amplitude." This argument is known somewhat widely around here, e.g. see this Less Wrong post by Paul Christiano, under "Born probabilities," and discussions of MWI and anthropic reasoning going back to the 190s (on the everything-list, in Nick Bostrom's dissertation, etc).

MWI would help in Solomonoff induction if there was some way of deriving the Born probabilities directly from the theory. Thus Eliezer's praise of Robin Hanson's mangled worlds idea. But at the moment there is no well-supported account of that type, as Eliezer admitted.

It's also worth distinguishing between complexity of physical laws, and anthropic penalties. Accounts of the complexity/prior of anthropic theories and measures to use in cosmology are more contested than simplicity of physical law. The Solomonoff prior implies some contested views about measure.