Heterogeneity in rates of trait evolution is widespread, but it remains unclear which processes drive fast and slow character divergence across global radiations. Here, we test multiple hypotheses for explaining rate variation in an ecomorphological trait (beak shape) across a globally distributed group (birds). We find low support that variation in evolutionary rates of species is correlated with life history, environmental mutagenic factors, range size, number of competitors, or living on islands. Indeed, after controlling for the negative effect of species' age, 80% of variation in species‐specific evolutionary rates remains unexplained. At the clade level, high evolutionary rates are associated with unusual phenotypes or high species richness. Taken together, these results imply that macroevolutionary rates of ecomorphological traits are governed by both ecological opportunity in distinct adaptive zones and niche differentiation among closely related species.