Humanoid robots, as general-purpose physical agents, must integrate both intelligent control and adaptive morphology to operate effectively in diverse real-world environments. While recent research primarily optimizes control policies for fixed bodies, we advocate body-control co-design as a path toward physical Recursive Self-Improvement (RSI): using experience from a humanoid's current body and policy to guide successive improvements to both. Inspired by biological evolution, this approach enables robots to recursively adapt both their form and behavior to optimize performance within task-specific and resource-constrained contexts. Despite its promise, co-design in humanoid robotics remains a relatively underexplored domain, raising fundamental questions about its feasibility and necessity in achieving true embodied intelligence. To address these challenges, we discuss potential co-design methodologies grounded in strategic exploration, Sim2Real transfer, and meta-policy learning. We further argue for the essential role of co-design by analyzing it from methodological, application-driven, and community-oriented perspectives. Striving to guide and inspire future studies, we present open research questions, spanning from short-term innovations to long-term goals. Ultimately, co-design offers a path toward physical RSI in humanoids that improves their bodies and policies while learning to make this improvement process more effective.

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