Just simulating the wave dynamics is not enough. You have to generate some further object from the waves, in order to get something in your simulation with the properties of reality. For example, you can repeatedly apply the Born rule as in Copenhagen to get a single stochastic history of particles, in which events occur with the appropriate frequencies. Or you could specify a deterministic rule for branching and joining, in which worlds are duplicated in different quantities at moments of branching in accordance with the Born rule, to create a deterministic multiverse in which events occur with the appropriate frequencies. Neither approach is very elegant; it's simpler to suppose that the waves are an incomplete statistical-mechanical description of something more fundamental (which, because of Bell's theorem, can't be a locally deterministic system in any obvious way, though it might be a local determinism whose variables are then transformed nonlocally to give conventional space-time).
But MWI advocates (at least of the Oxford variety) claim that the properties of reality emerge from the wavefunction. No additional "beables" are required. I know you disagree, but I'm pretty sure that's the sort of view Aaronson is referring to when he says MWI is mathematically simpler. The fundamental ontology is the wavefunction itself, not worlds of matter/energy whose multiplication is described by the wavefunction.
http://www.scottaaronson.com/blog/?p=1103
Eliezer's gung-ho attitude about the realism of the Many Worlds Interpretation always rubbed me the wrong way, especially in the podcast between both him and Scott (around 8:43 in http://bloggingheads.tv/videos/2220). I've seen a similar sentiment expressed before about the MWI sequences. And I say that still believing it to be the most seemingly correct of the available interpretations.
I feel Scott's post does an excellent job grounding it as a possibly correct, and in-principle falsifiable interpretation.