Short answer first, then the reasoning. The mechanism is slowed transit plus reduced intake, and that combination determines which interventions work. Less food means less bulk, slower motility means more water reabsorbed, and the result is a smaller, drier, slower stool. Insoluble fiber adds bulk to a system that is already moving slowly, which is why it frequently makes things worse. Soluble fiber holds water and is the better first choice, and an osmotic agent works with the mechanism rather than against it.
I would rather be corrected than agreed with, if it comes to it.