Very interesting discussion! Let me see whether I can contribute with something substantial.

I agree that, accepting the validity of a unitary quantum description for all of physical reality, the decoherence phenomenon is a property of this description, and collapse becomes an emergent phenomenon, occurring in certain open subsystems. What remains instead of coherence, however, is probability, more precisely the probabilities of different classical outcomes, and I think the question which Arnold Neumaier has raised, namely whether probability also is emergent in some sense, is a very interesting one.

Let me elaborate on this. Decoherence produces (locally) a set of decohered, effectively classical "histories" which, I believe, roughly can be identified with Everett's "many worlds". Quantum theory ascribes each of these a certain probability, instead of the certainty of classical reality which each of us experiences; and in each of the histories collapses will occur, together with an associated history branching. All of the histories are part of the unique "wave function of the universe", but once decohered, they do not dynamically influence each other anymore, and so our consciousness (like any physical process) cannot associate them with each other, i.e. we cannot be aware of more than one of them at a time. So, subjectively we always live in only one of "many worlds", and we experience all events that occur in it with certainty instead of probability (for instance, we observe the decay of a radioactive nucleus as an event which at any moment has either occured or not occurred instead of occurred with a certain probability). I believe this is also somehow the idea behind Wigner's "consciousness-induced collapse" and the "many-mind-interpretation".

On the other hand, collapses observed within a given history will then appear stochastic and happen (under suitably controlled conditions) with certain reproducible frequencies, interpreted by us as "quantum jump probabilities". Therefore this latter kind of "probability" is emergent from the underlying, continuous, decohering dynamics of the global "wave function of the universe".

As you can see from the above, my feeling is that the "many-words", "many-minds", and "consciousness-causes-collapse" (and perhaps also "consistent-histories") interpretations in some deeper sense all are equivalent and just different aspects of the same fundamental interpretation whose basic premise is to ascribe ontic reality to some quantum mechanical state representing all of reality (the "wave function of the universe").

One may consider it an attractive property of this world view is that it grants all possible histories of the world equal reality, so in a way our quantum mechanical universe is not just Leibniz's "best of possible worlds" but much more, namely something like the "totality of ALL possible (classical) worlds". Equally well, the same property may be considered repelling, since it displays such an incredible wastefulness, with innumerable "histories" we cannot communicate with, and thus violates Occam's principle to the largest possible degree.

Finally, my simple answers to Giulio's questions. 1. Do we need von Neumann's collapse as a physical process? No, I don't think so. 2. Do we need an interpretation of quantum physics? Sure we do, since the quantum mechanical state reductions leading to our unique classical reality must occur somewhere; even if we push them all the way up into the subjective mind of the observer, we cannot get rid of them altogether. And, even more fundamentally, we must decide whether we consider the quantum state ontic or epistemic, as user1247 has already pointed out repeatedly.