Abstract: The aim of goal-oriented materials design is to identify the appropriate chemical compositions and processing conditions required to obtain specific material properties. Traditionally, a material's microstructure serves two main roles: it is either employed in multiscale simulations to develop a reversible, quantitative relationship between process, structure, and property (PSP), or it is used to explain the microstructural characteristics that contribute to the attained properties after the fact. However, the design process itself often overlooks the microstructure, treating it merely as a mediator in the process-property (PP) relationship and rarely leveraging it directly in optimization, except in certain cases like architected materials. Despite the acknowledged importance of PSP relationships in materials science, it is commonly believed that focusing on PP relationships suffices for materials design. This study challenges this notion by introducing a novel, microstructure-informed, closed-loop, multi-fidelity Bayesian optimization framework for materials design. Through rigorous validation, we highlight the critical role of microstructure information in enhancing the design process. Our findings convincingly demonstrate the advantages of integrating microstructure insights into the materials design strategy. This research conclusively demonstrates, within a computational framework and through a specific example, that the PSP paradigm offers superior guidance for materials design compared to the PP approach, particularly in scenarios where microstructure significantly influences the material properties of interest.