  One of the goals of gravitational-wave astrophysics is to infer the number
and properties of the formation channels of binary black holes (BBHs); to do
so, one must be able to connect various models with the data. We explore
benefits and potential issues with analyses using models informed by population
synthesis. We consider 5 possible formation channels of BBHs, as in Zevin et
al. (2021b). First, we confirm with the GWTC-3 catalog what Zevin et al.
(2021b) found in the GWTC-2 catalog, i.e. that the data are not consistent with
the totality of observed BBHs forming in any single channel. Next, using
simulated detections, we show that the uncertainties in the estimation of the
branching ratios can shrink by up to a factor of $\sim 1.7$ as the catalog size
increases from $50$ to $250$, within the expected number of BBH detections in
LIGO-Virgo-KAGRA's fourth observing run. Finally, we show that this type of
analysis is prone to significant biases. By simulating universes where all
sources originate from a single channel, we show that the influence of the
Bayesian prior can make it challenging to conclude that one channel produces
all signals. Furthermore, by simulating universes where all 5 channels
contribute but only a subset of channels are used in the analysis, we show that
biases in the branching ratios can be as large as $\sim 50\%$ with $250$
detections. This suggests that caution should be used when interpreting the
results of analyses based on strongly modeled astrophysical sub-populations.
