Natural killer (NK) cells are innate immune cells that sense abnormal host cells through activating and inhibitory receptors. NK cells are early responders to viral infection. We previously found that SARS-CoV-2 (WA1) evades NK cell killing by downregulating the ligands for the activating receptor NKG2D (“NKG2D-L”). We also found that NKG2D-L downregulation depends on the viral protein Nsp1. This is consistent with the importance of Nsp1 as a global inhibitor of host cell translation. Whether Nsp1-mediated immune evasion is conserved in SARS-CoV-2 variants or other human coronaviruses (hCoVs) is largely unknown. In this study, we investigated the ability of NK cells to respond to SARS-CoV-2 variants, including Omicron/B.1.1.529, as well as other less pathogenic human coronaviruses (OC43 and 229E). We found that Omicron more effectively downregulates NKG2D-L compared to earlier strains of SARS-CoV-2 and identified a putative mechanism by which this occurs. Given the high degree of functional conservation of Nsp1 across hCoVs, we also assess the abilities of Nsp1 proteins from highly pathogenic versus less pathogenic hCoVs to mediate evasion of NK cell killing and determine that Nsp1s from highly pathogenic hCoVs are broadly more potent suppressors of NKG2D-L that those from less pathogenic hCoVs. Lastly, we demonstrate that, unlike SARS-CoV-2, the less pathogenic hCoVs OC43 and 229E are unable to evade NK cell killing. Together, our results collectively give rise to the hypothesis that increased susceptibility to the NK cell response may negatively correlate with hCoV pathogenicity and replicative fitness.