We report on the exciton propagation in polar (Al,Ga)N/GaN quantum wells over several micrometers and up to room temperature. The key ingredient to achieve this result is the crystalline quality of GaN quantum wells grown on GaN substrate that limits nonradiative recombination. From the comparison of the spatial and temporal dynamics of photoluminescence, we conclude that the propagation of excitons under continuous-wave excitation is assisted by efficient screening of the in-plane disorder. Modeling within drift-diffusion formalism corroborates this conclusion and suggests that exciton propagation is still limited by the exciton scattering on defects rather than by exciton-exciton scattering so that improving interface quality can boost exciton transport further. Our results pave the way towards room-temperature excitonic devices based on gate-controlled exciton transport in wide-band-gap polar heterostructures.