The hypothesis that low productivity has uniquely constrained Australia's large mammalian carnivore diversity, and by inference the biota in general, has become an influential backdrop to interpretations of ecology on the island continent. Whether low productivity has been primary impacts broadly on our understanding of mammalian biogeography, but investigation is complicated by two uniquely Australian features: isolation and the dominance of marsupials. However, until the great American biotic interchange (GABI), South America was also isolated and dominated by pouched carnivores. Here, we examine the low–productivity hypothesis empirically, by comparing large mammalian carnivore diversities in Australia and South America over the past 25 Myr. We find that pre–GABI diversity in Australia was generally comparable to or higher than diversity in South America. Post–GABI, South American diversity rose dramatically, pointing to isolation and phylogenetic constraint as primary influences. Landmass area is another important factor. Comparisons of diversity among the world's seven largest inhabited landmasses show that large mammalian hypercarnivore diversity in Australia approached levels predicted on the basis of landmass area in Late Pleistocene–Recent times, but large omnivore diversity was low. Large marsupial omnivores also appear to have been rare in South America. Isolation and competition with large terrestrial birds and cryptic omnivore taxa may have been more significant constraints in this respect. Relatively high diversity has been achieved in Late Quaternary America, possibly as a result of ‘artificially’ high immigration or origination rates, whereas that in contemporaneous Africa has been surprisingly poor. We conclude that isolation and landmass area, rather than productivity, are the primary constraints on large mammalian carnivore diversity. Our results quantify the rarity of large hypercarnivorous mammals worldwide.