The discovery of neutron stars powering several ultraluminous X-ray sources (ULXs) raises important questions about the nature of the underlying population. In this paper we build on previous work studying simulated populations by incorporating a model where the emission originates from a precessing, geometrically beamed wind-cone, created by a super-critical inflow. We obtain estimates – independent of the prescription for the precession period of the wind – for the relative number of ULXs that are potentially visible (persistent or transient) for a range of underlying factors such as the relative abundance of black holes or neutron stars within the population, maximum precessional angle, and LMXB duty cycle. We make initial comparisons to existing data using a catalogue compiled from XMM-Newton. Finally, based on estimates for the precession period, we determine how the eROSITA all-sky survey (eRASS) will be able to constrain the underlying demographic.