If other foods with fiber don't work, how do you know that it's even the fiber in sweet potato that makes you go?

A diet that leans more on fat and protein vs. carbohydrate should give lower insulin whether it's at weight loss levels or in maintenance. Low insulin foods might matter more in maintenance--especially if maintenance for you involves needing to take in more calories. Losing weight primes our system in various ways to get fat again, if the opportunity arises--and increasing insulin/carbs too far going into maintenance counts here as an opportunity.