In recent years, there has been a lot more attention towards the utilization of physically intelligent features in robotics. In this work, we provide a perspective on the physical artificial intelligence (PAI) paradigm and its impact on the conceptualization, design, and manufacturing of current and future aerial robots and infrastructure. We highlight the theory, enabling technologies, system features, and the tasks that the PAI paradigm will improve beyond the current approaches with conventional rigid aerial robots. We also discuss the multi-disciplinary effort required to collaborate with and educate researchers in the development of physically intelligent robots. PAI promises to lead the development of a new era of robust flying robotic organisms that are capable of adapting to and performing multi-functional tasks autonomously in a complex and unstructured environment. Aerial robotics is a great field of study to validate PAI as a development methodology.