Soft robotics is a rapidly growing area of robotics research that would benefit greatly from design automation, given the challenges of manually engineering complex, compliant, and generally non-intuitive robot body plans and behaviors. It has been suggested that a major hurdle currently limiting soft robot brain-body co-optimization is the fragile specialization between a robot's controller and the particular body plan it controls, resulting in premature convergence. Here we posit that modular controllers are more robust to changes to a robot's body plan. We demonstrate a decreased reduction in locomotion performance after morphological mutations to soft robots with modular controllers, relative to those with similar global controllers - leading to fitter offspring. Moreover, we show that the increased transferability of modular controllers to similar body plans enables more effective brain-body co-optimization of soft robots, resulting in an increased rate of positive morphological mutations and higher overall performance of evolved robots. We hope that this work helps provide specific methods to improve soft robot design automation in this particular setting, while also providing evidence to support our understanding of the challenges of brain-body co-optimization more generally.