Three- and four-year-olds are newly aware of being watched. The same child who happily pooped in a diaper in the living room now wants a closed door and nobody near. Preschool bathrooms are designed for supervision, not privacy, so the child's answer is to hold.
Schedules add to it. Pooping tends to want to happen after meals, but after lunch at preschool is usually a quick group toilet trip and then nap or outside play. The urge arrives, there is no quiet option, and it passes. By pickup the poop is larger and drier than it would have been.
Teachers see the edges of this: a child who gets quiet or clingy after lunch, who dances or crosses their legs, who hides in the book corner, or who has a small leak nobody can explain. Few connect it to holding, because a child who holds looks like a child who does not need to go.
Some preschools expect children to be fully trained and say so. In practice almost all can accommodate a short, written plan, especially one that asks for very little: a private toilet, a quiet time after lunch, and the same calm phrases you use at home.