In Verity's first paper on weak complicial sets, he shows that every strict complicial set is a weak complicial set. He also showed in an earlier paper that the full subcategory of stratified simplicial sets spanned by the strict complicial sets is equivalent to the category of globular strict $\omega$-categories.
A troubling corollary of these two facts together is that upon passing to the homotopy category, since all strict complicial sets are both fibrant and cofibrant, that all pseudofunctors between strict $\omega$-categories are representable by strict $\omega$-functors.
Is there a general coherence result for strict $n$-categories showing that indeed every pseudofunctor can be strictified up to a sufficiently weak notion of pseudonatural homotopy? (I am defining a pseudofunctor $A\to B$ of strict $n$-categories following Garner to be a strict $n$-functor $C(A)\to B$ where $C$ is the cofibrant replacement comonad arising from the Free-Forgetful adjunction to $n$-computads).
If not, has anyone conjectured a class of monomorphisms of stratified simplicial sets at which we could localize in order to obtain the correct model category?