The Pythagoreans believed that soul (greek: "psyche") was different from conscious sensation. Philolaus, for instance, wrote that the interaction of soul and body produced feeling. Soul referred to the immaterial nature of eternal reality — immaterial and eternal in the sense of mathematics. For instance, spheres and triangles are never perfectly instantiated in the material world, yet they are very real. This I find…
In other words embodyment is a necessity for consciousness. The ability to explore, interact, make experiments, test theories, they all depend on having an able body to move around and a rich environment to explore. A body also brings necessities - the agent needs to work to keep itself alive, and has goals, positive and negative rewards. These are ingredients without which there would be no point for consciousness to exist.