The binary neutron star merger gravitational-wave signal GW170817 was followed by three electromagnetic counterparts, including a kilonova arising from the radioactivity of freshly synthesized $r$-process elements in ejecta from the merger. Finding kilonovae after gravitational-wave triggers is crucial for (i) the search for further counterparts, such as the afterglow, (ii) probing the diversity of kilonovae and their dependence on the system's inclination angle, and (iii) building a sample for multi-messenger cosmology. During the third observing run of the gravitational-wave interferometer network, no kilonova counterpart was found. We aim to predict the expected population of detectable kilonova signals for the upcoming O4 and O5 observing runs of the LIGO-Virgo-KAGRA instruments. Using a simplified criterion for gravitational-wave detection and a simple GW170817-calibrated model for the kilonova peak magnitude, we determine the rate of kilonovae in reach of follow-up campaigns and their distributions in magnitude for various bands. We briefly consider the case of GW190425, the only binary neutron star merger confirmed since GW170817, and obtain constraints on its inclination angle from the non-detection of its kilonova, assuming the source was below the follow-up thresholds. We also show that non-gravitational-wave-triggered kilonovae can be a numerous class of sources in future surveys and briefly discuss associations with short bright gamma-ray bursts. We finally discuss the detection of the jetted outflow afterglow in addition to the kilonova.