Context. Many barriers prevent dust from forming planetesimals via coagulation in protoplanetary discs, such as bouncing, collisional fragmentation, or aeolian erosion. Modelling dust and the different phenomena that can alter its evolution is therefore necessary. Multiple solutions have been proposed, but they still need to be confirmed. Aims. In this paper, we explore the role that aeolian erosion plays in the evolution of dust. Methods. We used a mono-disperse model to account for dust growth and fragmentation, implemented in a 1D code to compute the evolution of single grains and in a 3D smoothed particle hydrodynamics (SPH) code to compute the global evolution of dust and gas. We tested the erosion model in our code and ensured it matched previous results. Results. With a disc model that reproduces observations, we show with both 1D and 3D studies that erosion is not significant during the evolution of dust when we take fragmentation into consideration. With a low-viscosity disc, fragmentation is less of a problem, but grain growth is also less important, which prevents the formation of large objects. In dust traps, close to the star, erosion is also not impactful, even when fragmentation is turned off. Conclusions. We show in this paper that aeolian erosion is negligible when radial drift, fragmentation, and dust traps are taken into account and that it does not alter the dust evolution in the disc. However, it can have an impact on later stages, when the streaming instability forms large clumps close to the star, or when planetesimals are captured.