What are the scientific arguments against decoherence? What do up-to-date theoreticians think?
The problem with decoherence is that the underlying physics of the wave function is still profoundly non-local in the sense that regions of the wave function don't have a simple relationship with regions of physical space.
And yet, classically, the notion of locality pertains precisely to physical space and is deeply related to fundamental physics. In fact, locality is still fundamental to the formulation of quantum mechanical theories, even if the quantum mechanical description ends up having some non-local features. And there isn't any philosophical or physical intuition that resolves this disconnect.
Decoherence has a variety of other philosophical issues. In particular, it requires that we accept the idea of the wave function (something we never see or interact with directly, for which we have no direct evidence) as fundamental and real AND that we take our day to day experiences, upon which all of our physical sciences are based, as derived, perhaps even, in important ways, not really real. In any case, the actual theoretical terms in which decoherence actually resolves the measurement paradox aren't fully understood either mathematically or in terms of the fundamental ontological status of things.
I don't see why locality is a requirement. What is it that makes a theory with particles being points in a six-dimensional position-momentum space acceptable, but particles being complex-valued functions over a three dimensional space unacceptable?
> it requires that we accept the idea of the wave function (something we never see or interact with directly, for which we have no direct evidence) as fundamental and real AND that we take our day to day experiences, upon which all of our physical sciences are based, as derived, perhaps even, in important ways, not really real.
I see no issue in pure quantum states being fundamental. Our day to day experiences are not compatible with a number of things we hold to be true. Take the physics of fluids for example, it suggests that liquids are infinitely dividable, which we know to be false. In that sense, fluid physics is decidedly not real. But it can also be derived as a very good approximation of the underlying reality on larger scales, similarly to how classical theories are good approximations of the underlying quantum reality on larger scales.
I do realize that my interpretation requires decoherence to work such that the pure quantum states reduce to ones that are well approximated by classical theories, and I'm not sure if we have evidence that decoherence works this way.
And people do debate how to derive our single world experience from many worlds. It can’t be done without more assumptions.
Many in this field do accept it, but say the other worlds are not real (QBism, dBB).
But that position is philosophically weak, so those against many worlds still look for alternatives.
Decoherence doesn't give you single outcomes, but it gives you a classical probability distribution (like an enthropic ensemble) over pure quantum states, with the pure quantum states having reduced coherence (i.e. they 'look classical').
Classical probability distributions are nothing new, we don't need a many worlds interpretation to explain the butterfly effect.
Quantum states with a small amount of residual superposition also seem fine to me, as long as you are willing to accept that the world is ultimately quantum and not classical. That we don't see any quantum effects in daily life is just because the scales are too small, similar to how we don't observe relativistic effects because the scales are too large, or how we don't observe the atomicity of water. But in all these cases we can do experiments to reveal the true nature.
But at no point does one world even approximately emerge - it’s always many. I can say only the one I experience is real, but there’s no justification for it.
Your main problem though is thinking classically - you can't justify your theory by saying it can be reduced (after an infinite amount of time) to an old way of thinking. Classical probability is fraught with issues; just saying it’s always been acceptable isn’t true nor a rational argument.
Decoherence or more strongly environmental super-selection from something like electromagnetic scattering, results in a Classical probability distribution over the macroscopic observables or more accurately renders the algebra of classical properties Boolean. This means there is no interference between the terms and the probabilities are simply ignorance of facts which have occurred.
Once this superselection process has occurred the mathematical structure of macroscopic observables is just as it is in classical statistical mechanics. There's no need to read this as multiple worlds, although you can if you want to. If interference terms persisted you might have more of a case for Many Worlds. Even then though there are other ways of reading the formalism.
If you're not familiar with these terms I can explain.