  An advanced LIGO and Virgo's third observing run brought another binary
neutron star merger (BNS) and the first neutron-star black hole mergers. While
no confirmed kilonovae were identified in conjunction with any of these events,
continued improvements of analyses surrounding GW170817 allow us to project
constraints on the Hubble Constant ($H_0$), 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 $0.43^{+0.58}_{-0.26}$
($1.97^{+2.68}_{-1.2}$) for the Zwicky Transient Facility (Rubin Observatory).
