How can many species coexist in natural ecosystems remains a fundamental question in ecology. Theory suggests that competition for space and resources should maintain the number of coexisting species far below the staggering diversity commonly found in nature. A recent model finds that, when sublinear growth rates of species are coupled with competition, species diversity can stabilize community dynamics. This, in turn, is suggested to explain the coexistence of many species in natural ecosystems. In this brief note we clarify why the sublinear growth (SG) model does not solve the long standing paradox of species coexistence. This is because in the SG model coexistence emerges from an unrealistic property, in which species per-capita growth rate diverges at low abundance, preventing species from ever going extinct. When infinite growth at low abundance is reconciled with more realistic assumptions, the SG model recovers the expected paradox: increasing diversity leads to competitive exclusion and species extinctions.