The Osteostraci and Galeaspida are stem gnathostomes, occupying a key phylogenetic position for resolving the nature of the jawless ancestor from which jawed vertebrates evolved more than 400 million years ago. Both groups are characterized by the presence of rigid headshields that share a number of common morphological traits, in some cases hindering the resolution of their interrelationships and the exact nature of their affinities with jawed vertebrates. Here, we explore the morphological and functional diversity of osteostracan and galeaspid headshields using an innovative approach that combines geometric morphometrics and computational fluid dynamics, thereby constraining the underlying factors that promoted the evolution of their similar morphologies and informing on the ecological scenario under which jawed vertebrates emerged. Phylomorphospace, Mantel analysis and Stayton metrics demonstrate a high degree of homoplasy. Computational fluid dynamics reveals similar hydrodynamic performance among morphologically convergent species, indicating the independent acquisition of the same morphofunctional traits and, potentially, equivalent lifestyles. This confirms that a number of the characters typically used to infer the evolutionary relationships among galeaspids, osteostracans and jawed vertebrates are convergent in nature, potentially obscuring understanding of the assembly of the gnathostome bodyplan. Ultimately, our results reveal that while the jawless relatives of the earliest jawed vertebrates were ecologically diverse, widespread convergence on the same hydrodynamic adaptations suggests they had reached the limits of their potential ecological diversity – overcome by jawed vertebrates and their later innovations.