  Compact-object binary mergers consisting of one neutron star and one black
hole (NSBHs) have long been considered promising progenitors for gamma-ray
bursts, whose central engine remains poorly understood. Using
gravitational-wave constraints on the population-level NSBH mass and spin
distributions we find that at most $20~\mathrm{Gpc}^{-3}\mathrm{yr}^{-1}$ of
gamma-ray bursts in the local universe can have NSBH progenitors.
