Decarbonizing the global steel industry hinges on three key limited resources: geological carbon storage, zero-emission electricity and end-of-life scrap. Existing system analysis calls for an accelerated expansion of the supply of these resources to meet the assumed ever-increasing steel demand. In this study, we propose a different view on how to decarbonize the global steel industry, based on the principle that resource supply can only expand in line with historical trends and actual construction plans. Our analysis shows that global steel production cannot grow any further within a Paris-compatible carbon budget, resulting in a shortfall of approximately 30% against 2050 demand. This trajectory involves the phasing out of blast furnaces, along with strong growth in scrap recycling and hydrogen-based production. These findings highlight critical yet often overlooked challenges: (i) reducing excess demand while providing essential services, (ii) producing high-grade steel through upcycling scrap, and (iii) ensuring an equitable distribution of limited production across the globe. These perspectives contrast with those of the current agenda, which largely emphasizes the need to invest in new production technologies. Grounded in a physical basis, this analysis offers a complementary perspective for a more balanced debate in policymaking and industrial strategy. This article is part of the discussion meeting issue 'Sustainable metals: science and systems'.