[ibab]

Yes, you are right to point this out. There are some important details that are still being debated. Personally my impression is that the debate has advanced enough to the point where MWI can’t be outright dismissed based on this argument. There are multiple plausible explanations and the remaining difficulties have more to do with philosophy than physics.

Edit: To give one example of an approach that I think is promising: We start by describing the observer and environment through a density matrix (a probability distribution over possible wave functions) and introduce an interaction with a quantum system (e.g. a spin). Given a reasonable interaction, you can show that the entanglement in the combined state (observer, environment and spin) leads to the system approaching a state that is a probability distribution of entangled states where each probability corresponds to the Born rule. Interestingly in this case the probabilities emerge from our lack of knowledge about the microstate of the observer/environment, so it’s actually thermodynamic uncertainty.

[Jweb_Guru]

I'm not dismissing MWI, I'm just saying that current formulations either don't reproduce quantum mechanics or don't really address the existence of randomness within quantum mechanics.

[Jweb_Guru]

While I intuitively like the statistical approach you mention, under it the Born rule holds only approximately, so it should be theoretically possible to observe entangled states which we have never done--i.e. it produces different predictions from the Copenhagen interpretation of quantum mechanics, which means it's not strictly a different interpretation, but its own falsifiable theory. Like I said in another comment, if we ever do observe entangled states directly, people will jump on board one of these alternate explanations like lightning. But until we do, the question of why we never ever observe anything that doesn't look like collapse still needs mathematical justification.