  The DESI collaboration have recently analyzed their first year of data,
finding a preference for thawing dark energy scenarios when using parameterized
equations of state for dark energy. We investigate whether this preference
persists when the data is analyzed within the context of a well-studied field
theory model of thawing dark energy, exponential quintessence. No preference
for this model over $\Lambda$CDM is found, and both models are poorer fits to
the data than the Chevallier-Polarski-Linder $w_0$--$w_a$ parameterization. We
demonstrate that the worse fit is due to a lack of sharp features in the
potential that results in a slowly-evolving dark energy equation of state that
does not have enough freedom to simultaneously fit the combination of the
supernovae, DESI, and cosmic microwave background data. Our analysis provides
guidance for constructing dynamical dark energy models that are able to better
accommodate the data.
