  A primary goal of the upcoming Deep Underground Neutrino Experiment (DUNE) is
to measure the $\mathcal{O}(10)$ MeV neutrinos produced by a Galactic
core-collapse supernova if one should occur during the lifetime of the
experiment. The liquid-argon-based detectors planned for DUNE are expected to
be uniquely sensitive to the $\nu_e$ component of the supernova flux, enabling
a wide variety of physics and astrophysics measurements. A key requirement for
a correct interpretation of these measurements is a good understanding of the
energy-dependent total cross section $\sigma(E_\nu)$ for charged-current
$\nu_e$ absorption on argon. In the context of a simulated extraction of
supernova $\nu_e$ spectral parameters from a toy analysis, we investigate the
impact of $\sigma(E_\nu)$ modeling uncertainties on DUNE's supernova neutrino
physics sensitivity for the first time. We find that the currently large
theoretical uncertainties on $\sigma(E_\nu)$ must be substantially reduced
before the $\nu_e$ flux parameters can be extracted reliably: in the absence of
external constraints, a measurement of the integrated neutrino luminosity with
less than 10\% bias with DUNE requires $\sigma(E_\nu)$ to be known to about 5%.
The neutrino spectral shape parameters can be known to better than 10% for a
20% uncertainty on the cross-section scale, although they will be sensitive to
uncertainties on the shape of $\sigma(E_\nu)$. A direct measurement of
low-energy $\nu_e$-argon scattering would be invaluable for improving the
theoretical precision to the needed level.
