CrN belongs to a family of transition metal nitrides used as protective coatings. It has an antiferromagnetic (AFM) orthorhombic structure below the Néel temperature (T _N) and adopts paramagnetic (PM) cubic B1 above T _N. In the past, the PM state was often wrongly approximated by a non-magnetic (NM) configuration. First-principles calculations suggested interesting mechanical properties of this hypothetical NM-CrN phase. In this work, we use density functional theory to probe the hypothesis that alloying or spatial confinement can cause local quenching of the Cr magnetic moments and, hence, stabilize the NM-CrN phase. Our calculations show that the magnetic moments are extremely robust and remain almost intact irrespective of which of the group III B to group VI B elements is alloyed. Similarly, superlattices with AlN and TiN in various thickness ratios do not reveal any quenching of the local magnetic moments. We therefore conclude that it is unlikely that material design would promote the NM-CrN phase, which thereby remains a purely hypothetical construct.