Understanding anthropogenic impacts on ecosystems requires investigating feedback processes between ecological and economic dynamics. While network ecology has advanced our understanding of large-scale communities, it has not robustly coupled economic drivers of anthropogenic impact to ecological outcomes. Leveraging allometric trophic network models, we study such integrated economic-ecological dynamics in the case of fishery sustainability. We incorporate economic drivers of fishing effort into food-web network models, evaluating the dynamics of thousands of single-species fisheries across hundreds of simulated food webs under fixed-effort and open-access management strategies. Analyzing simulation results reveals that harvesting species with high population biomass can initially support fishery persistence but threatens long-term economic and ecological sustainability by indirectly inducing extinction cascades in non-harvested species. This dynamic is exacerbated in open-access fisheries where profit-driven growth in fishing effort increases perturbation strength. Our results demonstrate how network theory provides necessary ecological context when considering the sustainability of economically dynamic fishing effort.