Cells of epithelial tissue proliferate and pack together to attain an eventual density homeostasis. As the cell density increases, spatial distribution of velocity and force show striking similarity to the dynamic heterogeneity observed elsewhere in dense granular matter. While the physical nature of this heterogeneity is somewhat known in the epithelial cell monolayer, its biological relevance and precise connection to cell density remain elusive. Relevantly, we had demonstrated how large-scale dynamic heterogeneity in the monolayer stress field in the bulk could critically influence the emergence of leader cells at the wound margin during wound closure, but did not connect the observation to the corresponding cell density. In fact, numerous previous reports had essentially associated long-range force and velocity correlation with either cell density or dynamic heterogeneity, without any generalization. Here, we attempted to unify these two parameters under a single framework and explored their consequence on the dynamics of leader cells, which eventually affected the efficacy of collective migration and wound closure. To this end, we first quantified the dynamic heterogeneity by the peak height of four-point susceptibility. Remarkably, this quantity showed a linear relationship with cell density over many experimental samples. We then varied the heterogeneity, by changing cell density, and found this change altered the number of leader cells at the wound margin. At low heterogeneity, wound closure was slower, with decreased persistence, reduced coordination and disruptive leader-follower interactions. Finally, microscopic characterization of cell-substrate adhesions illustrated how heterogeneity influenced orientations of focal adhesions, affecting coordinated cell movements. Together, these results demonstrate the importance of dynamic heterogeneity in epithelial wound healing. This article is part of the theme issue 'Multi-scale analysis and modelling of collective migration in biological systems'.