> In fact, there is no randomness and non-predictability in quantum mechanics.
Depends on the interpretation.
> wave function collapse in a quantum system is the consequence of coupling the system to a larger, external one that becomes entangled with the "small" quantum system
Depends on the interpretation.
> we ourselves are described by a quantum wave function
Depends on the interpretation.
> Different interpretations of quantum mechanics like the "Many Worlds" or the "Copenhague" varieties are basically just arguing about what happens with a wave function after it "collapses".
You only really need to worry about "what happens with a wave function" if you have a decidedly psi-ontic view of it. Otherwise, collapse is not itself a physical process.
> To my knowledge there is no way to discriminate between different alternatives here
The same author recently uploaded a paper which argues that there is a way to discriminate between interpretations based on physical principles. See http://arxiv.org/pdf/1509.03641v1.pdf .
Decoherence can explain the diagonalization of the density matrix: it takes a state to a mixture of eigenstates. However "the collapse of the wavefunction" induced by a measurement selects a single eigenstate. Decoherence does not explain that. For example it cannot explain the Born rule.
The actual Born rule is approximately explained by decoherence + GRW.
So decoherence + simple ontology is a great way to avoid the vagueness that Copenhagen gives you.
Unfortunately, this picture is almost completely wrong. In fact, there is no randomness and non-predictability in quantum mechanics. The fact that we observe wave function collapse in a quantum system is the consequence of coupling the system to a larger, external one that becomes entangled with the "small" quantum system and -through so-called decoherence- produces what we call the collapse of the wave function to a "classical" state. This process is entirely deterministic.
The theory of such "open quantum systems" is well established today and explains many of the seeming paradoxes that have plagued quantum mechanics, and it also provides clear answers to many of the questions posed in the article.
Some questions, in particular what happens to the parts of the wave function that do not become part of our reality after a collapse cannot be answered by any known theoretical framework, hence different people will have different opinions concerning those. The problem here is that we ourselves are described by a quantum wave function and therefore "live" inside the quantum world, we can therefore not "step back" and look at a wave function from the outside, which is why we can't answer what happens with the parts of a wave function that correspond to measurement results that we have not obtained when measuring an observable of a quantum system. Different interpretations of quantum mechanics like the "Many Worlds" or the "Copenhague" varieties are basically just arguing about what happens with a wave function after it "collapses".
To my knowledge there is no way to discriminate between different alternatives here, the preferences that individual physicists have in this matter are therefore based more on personal belief or concepts like simplicity or "beauty", hence we should not waste time trying to find out which is the right one.