The fact that the same proportionalities rule optimal running, flying and swimming is not a coincidence rather it is an illustration of the fact that a universal principle is involved.
Serendipity is the way to make discoveries, by accident but also by sagacity, of things one is not in quest of. Based on experience, knowledge, it is the creative exploitation of the unforeseen.
Flow systems have two basic features (properties). There is the current that is flowing (for example, fluid, heat, mass, or information) and the design through which it flows.
The similarities among animals that are on the surface very different are no coincidence. In fact, animal locomotion is no different than other flows, animate and inanimate they all develop in space and in time such that they optimize the flow of material.
For a finite-size system to persist in time (to live), it must evolve in such a way that it provides easier access to the imposed currents that flow through it.