Okay, let me try another tack.

One of the last greatest open questions in quantum mechanics, and the only one that seems genuinely mysterious, is where the Born statistics come from - why our probability of seeing a particular result of a quantum experiment, ending up in a particular decoherent blob of the wavefunction, goes as the squared modulus of the complex amplitude.

Is it the case that the Born probabilities are necessarily explained - can only be explained - by some hidden component of our brain which says that we care about the alternatives in proportion to their squared modulus?

Since (after all) if we only cared about results that went a particular way, then, from our perspective, we would always anticipate seeing the results go that way? And so what we anticipate seeing, is entirely and only dependent on what we care about?

Or is there a sense in which we end up seeing results with a certain probability, a certain measure of ourselves going into those worlds, regardless of what we care about?

If you look at it closely, this is really about an instantaneous measure of the weight of experience, not about continuity between experiences. But why don't the same arguments on continuity work on measure in general?