We explore the notion that cosmological models that modify the late-time expansion history cannot simultaneously fit the SH0ES collaboration’s measurements of the Hubble constant, DESI baryon acoustic oscillations data, and Type Ia supernova distances. Adopting a few simple phenomenological models, we quantitatively demonstrate that a satisfactory fit with a model with late-time expansion history can only be achieved if one of the following is true: 1) there is a sharp step in the absolute magnitude of Type Ia supernovae at very low redshift, $z\sim 0.01$, or 2) the distance duality relation, $d_L(z)=(1+z)^2d_A(z)$, is broken. Both solutions are trivial in that they effectively decouple the calibrated SNIa measurements from other data, and this qualitatively agrees with previous work built on studying specific dark-energy models. We also identify a less effective class of late-time solutions with a transition at $z\simeq 0.15$ that lead to a more modest improvement in fit to the data than models with a very low-z transition. Our conclusions are largely unchanged when we include surface brightness fluctuation distance measurements, with their current systematic uncertainties, to our analysis. We finally illustrate our findings by studying a physical model which, when equipped with the ability to smoothly change the absolute magnitude of Type Ia supernovae, partially resolves the Hubble tension.