> Decoherence explains why each state of the observer can't tell that the other states also exist.
Sure, but, again, decoherence doesn't explain (1) why the wave function is split in the classical states (position, momentum etc.) and not other states (linear combinations of position and momentum and spin etc.); and (2) doesn't explain why different states have the precise probabilities of being observed that they do. You still need to postulate these features.
> Sure, except we have to invent an entirely new non-unitary transformation of "collapse" despite all observations and predictions of quantum mechanics showing that unitary evolution of the wavefunction continues even for large macro-scale objects.
You're confusing the map for the territory. What we can see, plain as day, is that unitary evolution of the wavefunction does not continue for macro-scale objects. MWI explains this through the framework of the universal wavefunction and its mutually un-interacting "branches", CI explains it through wavefunction collapse. No one has ever successfully put a macroscopic object in superposition, so the idea that the universe itself could be in superposition remains highly theoretical at best.
Note also that movement in the classical world (and in GR) is often highly non-linear/non-unitary (such as the movement of a free pendulum, or many kinds of orbits). While far from perfect for this, the Born rule at least allows us to "sneak in" non-unitary evolution through this collapse; but, in the MWI, we predict that the movement of a free pendulum should in fact be non-chaotic. This is rarely discussed, but is an interesting observation that could be experimentally tested as we get better at creating larger and larger systems that remain coherent for longer and longer periods of time.