The design (shape) of a robot is usually decided before the control is implemented. This might limit how well the design is adapted to a task, as the suitability of the design is given by how well the robot performs in the task, which requires both a design and a controller. The co-optimization or simultaneous optimization of the design and control of robots addresses this limitation by producing a design and control that are both adapted to the task. In this paper, we investigate some of the challenges inherent in the co-optimization of design and control. We show that retraining the controller of a robot with additional resources after the co-optimization process terminates significantly improves the robot's performance. In addition, we demonstrate that the resources allocated to training the controller for each design influence the design complexity, where simpler designs are associated with lower training budgets. The experimentation is conducted in four publicly available simulation environments for co-optimization of design and control, making the findings more applicable to the general case. The results presented in this paper hope to guide other practitioners in the co-optimization of design and control of robots.