Think of it this way - decoherence depends on regions of the wave function more or less becoming isolated from one another in such a way that the results of experiments for classical things in those regions match our results. The wave function is still fundamental, but classical physics emerges as a limit.

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.