I hope somebody will correct me if I'm wrong, but it seems that the simplest way to phrase the main objection is that decoherence doesn't even try to solve anything beyond "for all practical purposes."
Fine: just imagine that we're sufficiently advanced to make it "practical" to track all the degrees of freedom for the system in question. Then it's clear that decoherence is just a fancy word for simple entanglement, and we're back at square one.
I admit it could have been phrased more clearly, but one comment says "If you have a new question, please ask it by clicking the Ask Question button" and another says "This does not provide an answer to the question." I don't think either applies.
It seems to me that it does answer the question. A strong objection to the claim that decoherence solves collapse is that it intends to solve it only "for all practical purposes" (FAPP), which is easily overcome by having enough "practical" ability to track and control all relevant entanglements.
For example, Penrose:
Under normal circumstances, one must regard the density matrix as some kind of approximation to the whole quantum truth. For there is no general principle providing an absolute bar to extracting information from the environment.[...] Accordingly, such descriptions are referred to as FAPP [For All Practical Purposes]
Maybe a future technology could provide means whereby quantum phase relations can be monitored in detail, under circumstances where present-day technology would simply ‘give up’. It would seem that the resort to a density-matrix description is a technology-dependent prescription! With better technology, the state- vector description could be maintained for longer, and the resort to a density matrix put off until things get really hopelessly messy!
Is there a way to contact the members who marked it for deletion and ask for clarification? Is that an appropriate course of action? Is there any sense in asking for undeletion?