Parametrization of galaxy morphologies is a challenging task, for instance in shear measurements of weak gravitational lensing or investigations of formation and evolution of galaxies. The huge variety of different morphologies requires a parametrization scheme that is highly flexible and that accounts for certain morphological observables, such as ellipticity, steepness of the radial light profile and azimuthal structure. In this article, we revisit the method of sérsiclets, where galaxy morphologies are decomposed into a set of polar basis functions that are based on the Sérsic profile. This approach is justified by the fact that the Sérsic profile is the first-order Taylor expansion of any real light profile. We show that sérsiclets indeed overcome the modelling failures of shapelets in the case of early-type galaxies. However, sérsiclets implicate an unphysical relation between the steepness of the light profile and the spatial scale of the polynomial oscillations, which is not necessarily obeyed by real galaxy morphologies and can therefore give rise to modelling failures. Moreover, we demonstrate that sérsiclets are prone to undersampling, which restricts sérsiclet modelling to highly resolved galaxy images. Analysing data from the weak-lensing great08 challenge, we demonstrate that sérsiclets should not be used in weak-lensing studies. We conclude that although the sérsiclet approach appears very promising at first glance, it suffers from conceptual and practical problems that severely limit its usefulness. In particular, sérsiclets do not provide high-precision results in weak-lensing studies. Finally, we show that the Sérsic profile can be enhanced by higher order terms in the Taylor expansion, which can drastically improve model reconstructions of galaxy images. When orthonormalized, these higher order profiles can overcome the problems of sérsiclets, while preserving their mathematical justification. However, this method is computationally expensive.