The identification of the asgard archaea has fueled speculations regarding the nature of the archaeal host in eukaryogenesis and its level of complexity prior to endosymbiosis. Here, we analyzed the coding capacity of 150 eukaryotes, 1,000 bacteria, and 226 archaea, including the only cultured member of the asgard archaea. Clustering methods that consistently recover endosymbiotic contributions to eukaryotic genomes recover an asgard archaeal-unique contribution of a mere 0.3% to protein families present in the last eukaryotic common ancestor, while simultaneously suggesting that this group's diversity rivals that of all other archaea combined. The number of homologs shared exclusively between asgard archaea and eukaryotes is only 27 on average. This tiny asgard archaeal-unique contribution to the root of eukaryotic protein families questions claims that archaea evolved complexity prior to eukaryogenesis. Genomic and cellular complexity remains a eukaryote-specific feature and is best understood as the archaeal host's solution to housing an endosymbiont.