The focus of goal-oriented materials design is to find the necessary chemistry/processing conditions to achieve the desired properties. In this setting, a material’s microstructure is either only used to carry out multiscale simulations to establish an invertible quantitative process-structure-property (PSP) relationship, or to rationalize a posteriori the underlying microstructural features responsible for the properties achieved. The materials design process itself, however, tends to be microstructure-agnostic: the microstructure only mediates the process-property (PP) connection and is—with some exceptions such as architected materials—seldom used for the optimization itself. While the existence of PSP relationships is the central paradigm of materials science, it would seem that for materials design, one only needs to focus on PP relationships. In this work, we attempt to resolve the issue whether ‘PSP’ is a superior paradigm for materials design in cases where the microstructure itself cannot be (directly) manipulated to optimize materials’ properties. To this end, we formulate a novel microstructure-aware closed-loop multi-fidelity Bayesian optimization framework for materials design and rigorously demonstrate the importance of the microstructure information in the design process. The problem considered here involves finding the right combination of chemistry and processing parameters that maximizes a targeted mechanical property of a model dual-phase steel. Our results clearly show that an explicit incorporation of microstructure knowledge in the materials design framework significantly enhances the materials optimization process. We thus prove, in a computational setting, and for a particular representative problem where microstructure intervenes to influence properties of interest, that ‘PSP’ is superior to ‘PP’ when it comes to materials design.