Is there a favoured mathematical model of bacterial growth?
Some clarifications:
Commonly used models for bacterial isothermal growth curves (which represent the growth curve directly) are for example:

Exponential

Logistic

Generalized logistic


The Monod equation expresses how the growth rate changes with the availability of substrate see a related question here.
The Monod equation can be incorporated into an exponential growth model (differential equation) like this:
$$
\frac{dX}{dt}=\mu X
$$
with
$$
\mu = \mu_{max} \frac{[S]}{K_M+[S]}
$$
where $X$ is the biomass concentration and $[S]$ is the substrate concentration. Or into a logistic growth model:
$$
\frac{dX}{dt}=\mu X \left(1 - \frac{X}{X_{max}} \right)
$$
with
$$
\mu = \mu_{max} \frac{[S]}{K_M+[S]}
$$
where $X_{max}$ is the carrying capacity.
Other growth-substrate relations like Haldane which takes into account growth inhibition by the substrate can be used instead of Monod one.
Regarding this:

Is there something holding the synthetic biology community back from regularly reporting growth characteristics of their cells?

It depends on what branch of synthetic biology you are looking into. Model-based design engineering biology interpretation of synthetic biology goes around the DBTL cycle. In the DBTL cycle, there are always (at least) models of both growth and gene expression.