Advanced LIGO and Virgo's third observing run brought another binary neutron
star merger (BNS) and the first neutron-star black-hole (NSBH) mergers. While
no confirmed kilonovae (KNe) was identified in conjunction with any of these
events, continued improvements of analyses surrounding GW170817 allow us to
project constraints on the Hubble Constant (H0), the Galactic enrichment
from r-process nucleosynthesis, and ultra-dense matter possible from
forthcoming events. Here, we describe the expected constraints based on the
latest expected event rates from the international gravitational-wave network
(IGWN) and analyses of GW170817. We show the expected detection rate of
gravitational waves and their counterparts, as well as how sensitive potential
constraints are to the observed numbers of counterparts. We intend this
analysis as support for the community when creating scientifically-driven
electromagnetic follow-up proposals. During the next observing run O4, we
predict an annual detection rate of electromagnetic counterparts from BNS of
0.43−0.26+0.58 (1.97−1.2+2.68) for the Zwicky Transient
Facility (Rubin Observatory)