Much is made of the potential for persistent identifiers (PIDs) to create efficiencies, aid discovery, and improve attribution and acknowledgements. Publishers have been at the forefront of PID adoption, from DOIs for articles to ORCID IDs for authors and reviewers. However, publishers are yet to fully realise the range of benefits PIDs could bring, especially in terms of their value in supporting open research. We present a life-cycle illustration of the benefits of PIDs, derived from a cost-benefit analysis we conducted for Jisc in the UK. The study identified significant benefits for publishers in streamlining internal information management, reducing administrative overhead, and improving the efficiency of submission processes (including payment of APCs) - not to mention improving the author experience. These improvements would enhance the integrity of publishing workflows and add transparency, ultimately increasing trust in research and research outputs. We found that PIDs could save the UK research sector £5.67M over five years, even after significant research sector investment in PID adoption and integrations. Publishers will only get their share of these benefits if they can rely on funders and institutions to populate PID registries with accurate data to feed publishing processes. At the same time, by embedding PIDs throughout their workflows, in metadata, and in discovery and aggregation tools, publishers will help multiply the benefits of PIDs for institutions and funders. We present new - and concrete - evidence of the long-hoped-for benefits of a shared PID-enabled open infrastructure, including pointing the way to how to build those benefits into the publishing system. We make the case that more outreach, cooperation, and education is needed across publishing and beyond to deliver those benefits. Our proposed win-win approach would help build trust across all scholarly communications stakeholders, as well as saving everyone time, effort, and money.