Decoherence does not give you Many Worlds, or at least not unless you interpret it that way.

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.

I think when you add in the word "experience" you turn the physics problem into a philosophical one, and every pragmatic scientist wanders off to work on something else. Many worlds is totally sufficient for every question except for the nature of consciousness, and there are some very good reasons to believe that consciousness is non-empirical.

I don't see many-world arising from decoherence, please elaborate.

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.

So during decoherence you don’t have classical worlds - the probabilities interfere so you can’t ignore the other terms. Over time that interference reduces, but as you say never disappears completely.

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.

What are the issues with Classical probability relevant to accepting there being a single world?

But, uh, a single world experience is trivially compatible with many worlds — in every world, the human is in a pure state that corresponds to a normal human experience of continuously living in a single world. If we don't require the conscience to be a single supernatural entity that flows along the timeline, selecting a world to visit at every branching point, then... that's it? Nothing else that still needs to be explained?

I apologize for the naivite of my line of thinking but wouldn't the locality of Relativity slot in at that point? Other realities could all be real, but only a subset could be real/accessible from the perspective of a given measurement device. As a guy who reads popular books on the subject to fall asleep, that seems like the obvious place for the two theories to couple. What am I missing?