They also improve the voltage rating by using a different winding technique - if you compare to a single spool of the same overall size, the windings typically run back and forth in layers. The start & finish of each pair of layers are a lot of turns apart but directly on top of each other so minimal insulation between them.
The segmented former is wound one section at a time, then working from one end to another. The narrow segments mean only a few turns between any two wires in contact, so a vastly higher voltage rating is possible with the same wire insulation.