MWI actually postulates that coherence of the system is always preserved, even up to the level of the entire universe. It's only locally that decoherence seeps in, at some scales.

But still, the problem I was questioning was different: you are saying "there is one of us in each world". In fact, that is not what QM predicts: in QM, there is only one of us in the entire system described by the wave function, with different amplitudes in different states. A system with 1 electron with some amplitude < 1 in state A and some amplitude < 1 in state B is not the same as a system with 2 electrons, one with amplitude 1 in state A and another with amplitude 1 in state B.

So, if we took a detector that could measure state A or state B, we should expect that it detects state A with some amplitude and, simultaneously, state B with some other amplitude. Instead, MWI postulates that there are 2 detectors, one which measures state A with amplitude 1, and the other state B with amplitude 1 (in fact, it postulates an infinity of detectors, out of which some number measure state A and some measure state B, such that the Born rule predictions by "counting" detectors).

This is the part that remains unexplained.