Svatmarama makes an unusually specific claim for paschimottanasana. He says it drives the breath into the sushumna, the central channel of the yogic body, kindles the gastric fire and makes the belly lean. Those are the text's statements, recorded here as the text's and not repeated as effects.
The claim about the central channel is the one that shows what the posture chapter is for. In the physiology the hatha corpus assumes, the breath ordinarily runs in the two side channels, ida and pingala, and the whole apparatus of breath restraint, locks and seals exists to redirect it into the sushumna, which is what the tradition says opens the way to the states described in the later chapters. A posture credited with doing that work directly is being placed close to the centre of the system rather than treated as preliminary conditioning.
The gastric fire, agni, belongs to a related set of ideas in which digestion is the model for transformation generally, and heat is the agent of it. Claims about kindling that fire recur across the corpus and attach to several postures. Geoffrey Samuel's Origins of Yoga and Tantra sets out the development of the subtle body physiology these claims depend on, and reading the posture chapter with that framework in view makes clear that the manuals are not describing exercise with incidental religious language attached.