  Gravitational-wave (GW) observations of binary black-hole (BBH) coalescences
are expected to address outstanding questions in astrophysics, cosmology, and
fundamental physics. Realizing the full discovery potential of upcoming
LIGO-Virgo-KAGRA (LVK) observing runs and new ground-based facilities hinges on
accurate waveform models. Using linear-signal approximation methods and
Bayesian analysis, we start to assess our readiness for what lies ahead using
two state-of-the-art quasi-circular, spin-precessing models:
\texttt{SEOBNRv5PHM} and \texttt{IMRPhenomXPHM}. We ascertain that current
waveforms can accurately recover the distribution of masses in the LVK
astrophysical population, but not spins. We find that systematic biases
increase with detector-frame total mass, binary asymmetry, and spin-precession,
with most such binaries incurring parameter biases, extending up to redshifts
$\sim3$ in future detectors. Furthermore, we examine three ``golden'' events
characterized by large mass ratios, significant spin magnitudes, and high
precession, evaluating how systematic biases may affect their scientific
outcomes. Our findings reveal that current waveforms fail to enable the
unbiased measurement of the Hubble-Lema\^itre parameter from loud signals, even
for current detectors. Moreover, highly asymmetric systems within the lower BH
mass-gap exhibit biased measurements of the secondary-companion mass, which
impacts the physics of both neutron stars and formation channels. Similarly, we
deduce that the primary mass of massive binaries ($ > 60 M_\odot$) will also be
biased, affecting supernova physics. Future progress in analytical calculations
and numerical-relativity simulations, crucial for calibrating the models, must
target regions of the parameter space with significant biases to develop more
accurate models. Only then can precision GW astronomy fulfill the promise it
holds.
