Among all these comments, I see no appreciation of the fact that the version of many worlds we have just been given CANNOT MAKE PREDICTIONS, whereas "collapse theories" DO.

Yes, Schrödinger evolution plus collapse is more complicated than just Schrödinger evolution. But the former makes the predictions, and the latter does not. We have been given the optimistic assertion that maybe the predictions are already somewhere inside the theory without collapse, but this remains to be shown. That's what the meaning of this whole "quest for the Born probabilities" is about! It is, precisely, the quest to restore the predictive capacity of quantum mechanics after you've taken collapse away. And the fact that it's a quest tells you that this is a research program whose goal is not accomplished.