In this paper, we address the question of why cluster radio relics that are connected to shock acceleration, so-called radio gischt relics, have preferentially been found in the outskirts of galaxy clusters. By identifying merger shock waves in cosmological grid simulations, we explore several prescriptions for relating the energy dissipated in shocks to the energy emitted in the radio band. None of the investigated models produces detectable radio relics within 100–200 kpc from the cluster centre. All models cause >50 per cent of the detectable relic emission at projected distances >800 kpc. Central radio relics caused by shocks that propagate along the line of sight are rare events for simple geometrical reasons, and they have a low surface brightness making them elusive for current instruments. Our simulations show that the radial distribution of observed relics can be explained by the radial trend of dissipated kinetic energy in shocks, which increases with distance from the cluster centre up until half of the virial radius.