The paucity of detectable seismicity shadows in the days/months following a main shock has raised the question as to whether dynamic rather than static triggering could be the main mechanism driving the seismicity at these timescales. The lack of correlation between the stress unloading of the main fault and the typically vigourous aftershock production taking place on it, however, suggests that the spatial heterogeneity of the coseismic stress change could also be a factor in the apparent suppression of seismicity shadows, at least on the main fault. Here we study whether this stress variability can indeed be an important aspect in the stress modeling of earthquake sequences. A rate-and-state friction model of seismicity is used, in conjunction with realistic levels of stress heterogeneity at the earthquake nucleation scale (1--10 m, as predicted from these friction laws), based on scale-invariant models of coseismic slip distribution. In this model, a relatively weak on-fault quiescence is delayed by months to years because of the high stress heterogeneity. Delayed quiescences due to slip heterogeneity are similarly predicted at distances of up to about half the rupture length away from the fault. We also postulate that off-fault seismicity can be significantly controlled by stress variability that originates from small-scale crustal heterogeneity and the complexity in fault geometries. Rather than mapping stress changes by providing a single stress value at every grid point, these results suggest that an estimate of the likely stress variability (acting at the nucleation scale) is also needed, especially when trying to account for the seismicity occurring at relatively short timescales.