It seem fairly obvious that science can reject many models of special creation. It cannot, however, reject all classes of special creation. If such a model is well motivated from theology, and incidentally produces a pattern matching common descent, it could be plausible.
That is why I say that science tells us definitively that it certainly appears as if common descent is true.
From a theological point of view, there is not a good argument against it. The best arguments focus on the historical Adam, and assume this is incompatible with evolution. We have shown, however, that this assumption is not warranted. If we can reconcile the common descent of man with Genesis 2, I see not plausible theological objection to the rest of common descent.
To the point, I know of good theologically coherent system in which we could accept the common descent of man, but then simultaneously reject the common descent of all animals. So, having solved the hard problem of a literal Adam and evolution, I’m not sure a valid theological case can be marshaled to insist on rejecting common descent.
I think the only reason common descent comes up is because it can be transmuted to universal common descent, where the data is the weakest. This is really just a smoke screen. The central theological challenge is really Adam, and the Genealogical Adam solves this problem directly.