While naturally occurring swarms thrive when crowded, physical interactions in robotic swarms are either avoided or carefully controlled, thus limiting their operational density. In this paper, we explicitly consider dense swarms of robots where physical interactions are inevitable. By leveraging collisions, we offer new applications in collective self-organization using a morpho-functional design. We demonstrate experimentally that an a priori minor difference in the mechanical design of the robots leads to major differences in their collective behavior when they evolve in crowded environments. We design Morphobots, which are Kilobots augmented with a 3D-printed exoskeleton. The exoskeleton not only significantly improves the motility and stability of the Kilobots, it also allows to encode two contrasting dynamical behaviors in response to an external force or a collision. This difference translates into distinct performances at the individual and collective behaviour. These include response to an external force, interaction with a stationary wall, alignment with a movable obstacle, stabilization on a dynamically tilting plane, and self-organized aggregation when addressing a phototactic task. Enabling collisions also fluidizes the ensemble allowing the implementation of a decentralized on-line evolutionary reinforcement learning algorithm in a swarm of Morphobots. Finally we present a kinetic model that links the reward function to an effective phototactic policy. Our results are of relevance for the deployment of robust swarms of robots in a real environment, where robots are deemed to collide, and to be exposed to external forces.