Indeed there is no such coherence result: it is false already for $2$-categories (see for instance Lemma 2 of this paper of Steve Lack). The solution to your troubling corollary is that the "correct" models for weak $\omega$-categories are not the weak complicial sets but the saturated weak complicial sets, i.e. those weak complicial sets in which all the equivalences are marked. In the Street nerve of a strict $\omega$-category, only the identities are marked, and it is thus not saturated in general (unless it has no non-identity equivalences, in which case all pseudofunctors into it are strict).

The saturated weak complicial sets are indeed the fibrant objects of a model structure on the category of stratified simplicial sets, which is a localisation of the model structure whose fibrant objects are the weak complicial sets. See Emily Riehl's lecture notes Complicial sets, an overture, in particular Example 3.3.5.

Indeed there is no such coherence result: it is false already for $2$-categories (see for instance Lemma 2 of this paper of Steve Lack). The solution to your troubling corollary is that the "correct" models for weak $\omega$-categories are not the weak complicial sets but the saturated weak complicial sets, i.e. those weak complicial sets in which all the equivalences are marked. In the Street nerve of a strict $\omega$-category only the identities are marked, and it is thus not saturated in general (unless the $\omega$-category has no non-identity equivalences, in which case all pseudofunctors into it are strict).

The saturated weak complicial sets are indeed the fibrant objects of a model structure on the category of stratified simplicial sets, which is a localisation of the model structure whose fibrant objects are the weak complicial sets. See Emily Riehl's lecture notes Complicial sets, an overture, in particular Example 3.3.5.

Indeed there is no such coherence result: it is false already for $2$-categories (see for instance Lemma 2 of this paper of Steve Lack). The solution to your troubling corollary is that the "correct" models for weak $\omega$-categories are not the weak complicial sets but the saturated weak complicial sets, i.e. those weak complicial sets in which all the equivalences are marked. In the Street nerve of a strict $\omega$-category, only the identities are marked, and it is thus not stratified in general (unless it has no non-identity equivalences, in which case all pseudofunctors into it are strict).

The saturated weak complicial sets are indeed the fibrant objects of a model structure on the category of stratified simplicial sets, which is a localisation of the model structure whose fibrant objects are the weak complicial sets. See Emily Riehl's lecture notes Complicial sets, an overture, in particular Example 3.3.5.

Indeed there is no such coherence result: it is false already for $2$-categories (see for instance Lemma 2 of this paper of Steve Lack). The solution to your troubling corollary is that the "correct" models for weak $\omega$-categories are not the weak complicial sets but the saturated weak complicial sets, i.e. those weak complicial sets in which all the equivalences are marked. In the Street nerve of a strict $\omega$-category, only the identities are marked, and it is thus not saturated in general (unless it has no non-identity equivalences, in which case all pseudofunctors into it are strict).

The saturated weak complicial sets are indeed the fibrant objects of a model structure on the category of stratified simplicial sets, which is a localisation of the model structure whose fibrant objects are the weak complicial sets. See Emily Riehl's lecture notes Complicial sets, an overture, in particular Example 3.3.5.