A genus is a taxonomic unit that may contain one species (monotypic) or thousands. Yet counts of genera or families are used to quantify diversity where species-level data are not available. High frequencies of monotypic genera (~30% of animals) have previously been scrutinised as an artefact of human classification. To test whether Linnean taxonomy conflicts with phylogeny, we compared idealised phylogenetic systematics in silico with real-world data. We generated highly-replicated, simulated phylogenies under a variety of fixed speciation/extinction rates, imposed three independent taxonomic sorting algorithms on these clades (2.65x10^8 simulated species), and compared the resulting genus size data with quality-controlled taxonomy of animal groups (2.8x10^5 species). ‘Perfect’ phylogenetic systematics arrives at similar distributions to real-world taxonomy, regardless of the taxonomic algorithm. Rapid radiations occasionally produce a large genus when speciation rates are favourable; however, small genera can arise in many different ways, from individual lineage persistence and/or extinctions creating subdivisions within a clade. The consistency of this skew distribution in simulation and real-world data indicates that specific aspects of its mathematical behaviour could be developed into generalised or nomothetic principles of the global frequency distributions of higher taxa. Importantly, Linnean taxonomy is a better-than-expected reflection of underlying evolutionary patterns.