Context. Many barriers prevent dust to form 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 needed. Multiple solutions have been proposed, but still need to be confirmed. Aims. In this paper, we explore the role aeolian erosion plays in the evolution of dust. Methods. We use a monodisperse model to account for dust growth and fragmentation, implemented in a 1D model to compute the evolution of single grains and a 3D SPH code to compute the global evolution of dust and gas. We test the erosion model in our code and ensured it matches previous results. Results. With a model of disc reproducing 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, preventing the formation of large objects anyway. 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 does not alter the dust evolution in the disc. However, it can have an impact on later stages, i.e. when the streaming instability forms large clumps close to the star, or when planetesimals are captured.