I think that's largely an implementation detail, so not a requirement as far as I know. That said, delimited continuations certainly make them easier to implement, as I understand it.
I guess it's a good marketing move because "multi-prompt delimited continuations" is scary. It also makes the types sane; I once worked out that expressions with delimited continuations of the reset-shift0 variety are typed by binary trees of ambient types, with a subtyping relation s.t. leaf nodes can be expanded.