> It seems like retaining the information about all possible universes is kind of nonsensical; the volume of data is just too large.

Do you have to retain all the information? Perhaps a set of quantum events is more like a parameter into a function, and the return value is the universe state corresponding to that history. Yeah there's magical black box handwaving going on there but the point is when we literally have no idea, it's not entirely impossible that the quantum multiverse is sparsely populated and lazy loaded with nothing 'computed' into existence until it has to be.

EDIT: Mind, I'm not saying that it is this way. The validity of my proposal isn't the point. The point is that dismissing Many Worlds on the grounds of "too much information" involves assuming a lot of things we don't actually know.