Robotic performance emerges from the coupling of body and controller, yet it remains unclear when morphology-control co-design is necessary. We present a unified framework that embeds morphology and control parameters within a single neural network, enabling end-to-end joint optimization. Through case studies in static-obstacle-constrained reaching, we evaluate trajectory error, success rate, and collision probability. The results show that co-design provides clear benefits when morphology is poorly matched to the task, such as near obstacles or workspace boundaries, where structural adaptation simplifies control. Conversely, when the baseline morphology already affords sufficient capability, control-only optimization often matches or exceeds co-design. By clarifying when control is enough and when it is not, this work advances the understanding of embodied intelligence and offers practical guidance for embodiment-aware robot design.