We report on the impact of a probabilistic prescription for compact remnant masses and kicks on massive binary population synthesis. We find that this prescription populates the putative mass gap between neutron stars and black holes with low-mass black holes. However, evolutionary effects reduce the number of X-ray binary candidates with low-mass black holes, consistent with the dearth of such systems in the observed sample. We further find that this prescription is consistent with the formation of heavier binary neutron stars such as GW190425, but overpredicts the masses of Galactic double neutron stars. The revised natal kicks, particularly increased ultra-stripped supernova kicks, do not directly explain the observed Galactic double neutron star orbital period-eccentricity distribution. Finally, this prescription allows for the formation of systems similar to the recently discovered extreme mass ratio binary GW190814, but only if we allow for the survival of binaries in which the common envelope is initiated by a donor crossing the Hertzsprung gap, contrary to our standard model.