Although most fisheries assessment and management focuses on the status of individual stocks, and regulations are commonly established as single-species total allowable catch limits (TACs), much of the catch from global fisheries comes from mixed-stock fisheries where species cannot be harvested separately. We show that in some fisheries where TAC and catch of demersal fish stocks are tracked, the average fraction of TAC harvested ranges from 21% to 68% overall and is declining. This is, in part, related to efforts to protect all species from overfishing, leading to ‘choke species’, which limit fishing pressure on other target species. While some choke species arise from a mix of low and high-productivity species, others result from allocation processes, which can be aggravated by shifting distributions due to climate change. Underutilization of TACs can also result from market limitations, low value of individual species, undercapacity or management measures. Proposed methods for increasing long-term yield require species to be managed in stock groups, or allowing the abundance of some stocks to fall below target reference points. We suggest that the observed low and declining aggregate harvests are due, primarily, to the focus on single-stock sustainability measures, rather than performance of the fisheries in relation to potential overall yield. While there is a growing consensus that single-species management should be replaced by an ecosystem-based approach, this will require clear legislative directives regarding management of the trade-offs involved. Time series considered in this analysis do not extend beyond 2019.