What is the primary motivation for a saint, who is free from the cycle of birth and death, to take on a physical body?

The text from Chapter 43 makes it very clear that the motivation is purely altruistic. Saints, who are described as being free from the six-fold changes and always remaining in an unmanifest state, choose to become manifest for a singular purpose: "the salvation of devotees." It is with the "sole desire for the welfare of devotees" that they take on various avatars. As Chapter 43 highlights, this act of incarnation is a conscious choice made out of compassion, not a karmic compulsion. Their physical presence is a temporary manifestation to guide and uplift others, after which their spiritual attainment remains unaffected.