In general, computing all evolutions of all universes is much cheaper in terms of information requirements than computing just one particular, arbitrarily chosen evolution. Why? Because the Great Programmer's algorithm that systematically enumerates and runs all universes (with all imaginable types of physical laws, wave functions, noise etc.) is very short (although it takes time). On the other hand, computing just one particular universe's evolution (with, say, one particular instance of noise), without computing the others, tends to be very expensive, because almost all individual universes are incompressible, as has been shown above. More is less!
Many worlds. Suppose there is true (incompressible) noise in state transitions of our particular world evolution. The noise conveys additional information besides the one for initial state and physical laws. But from the Great Programmer's point of view, almost no extra information (nor, equivalently, a random generator) is required. Instead of computing just one of the many possible evolutions of a probabilistic universe with fixed laws but random noise of a certain (e.g., Gaussian) type, the Great Programmer's simple program computes them all. An automatic by-product of the Great Programmer's set-up is the well-known ``many worlds hypothesis'', ©Everett III. According to it, whenever our universe's quantum mechanics allows for alternative next paths, all are taken and the world splits into separate universes. From the Great Programmer's view, however, there are no real splits -- there are just a bunch of different algorithms which yield identical results for some time, until they start computing different outputs corresponding to different noise in different universes.
From an esthetical point of view that favors simple explanations of everything, a set-up in which all possible universes are computed instead of just ours is more attractive. It is simpler.