A new measurement of a spatially extended gamma-ray signal from the center of the Andromeda galaxy (M31) has recently been published by the Fermi-LAT collaboration, reporting that the emission broadly resembles the so-called Galactic center excess (GCE) of the Milky Way (MW). The weight of the evidence is steadily accumulating on a millisecond pulsar (MSPs) origin for the GCE. These elements prompt us to compare these observations with what is, perhaps, the simplest model for an MSP population, which is solely obtained by rescaling of the MSP luminosity function that is determined in the local MW disk via the respective stellar mass of the systems. Remarkably, we find that without free fitting parameters, this model can account for both the energetics and the morphology of the GCE within uncertainties. For M31, the estimated luminosity due to primordial MSPs is expected to only contribute about a quarter of the detected emission, although a stronger contribution cannot be excluded given the large uncertainties. If correct, the model predicts that the M31 disk emission due to MSPs is not far below the present upper bound. We also discuss additional refinements of this simple model. Using the correlation between globular cluster gamma-ray luminosity and stellar encounter rate, we gauge the dynamical MSP formation in the bulge. This component is expected to contribute to the GCE only at a level of 5%, it could affect the signal's morphology. We also comment on the limitations of our model and on future perspectives for improved diagnostics.