It’s the simplest explanation (in terms of Kolmogorov complexity).
It’s also the interpretation which by far has the most elegant explanation for the apparent randomness of reality. Most interpretations provide no mechanism for the selection of a specific outcome, which is absurd. Under the MWI, randomness emerges from determinism through indexical uncertainty, i.e., not knowing which branch you’re in. Some people, such as Sabine Hossenfelder for example, get confused by this and ask, “then why am I this version of me?”, which implicitly assumes dualism, as if there is a free-floating consciousness which could in principle inhabit any branch; this is patently untrue because you are by definition this “version” of you. If you were someone else (including someone in a different branch where one of your atoms is moved by one Planck distance) then you wouldn’t be you; you would be literally someone else.
Note that the Copenhagen interpretation is also a many-worlds explanation, but with the added assumption that all but one randomly chosen world disappears when an “observation” is made, i.e., when entanglement with your branch takes place.
I think that “rational, deliberate design”, as you put it, is simply far less common (than random chance) than you think; that the vast majority of human knowledge is a result of induction instead of deduction; that theory is overrated and experimentalism is underrated.
This is also why I highly doubt that anything but prosaic AI alignment will happen.