Does an elegant gown have to be a ballgown?

No. Elegance comes from cut, fabric, and proportion rather than from volume. Many of the most elegant wedding dresses are A-line, sheath, column, or modified mermaid silhouettes in fluid fabrics. Ballgowns can absolutely read elegant, especially in plain Mikado satin without heavy embellishment, but they are one option among several rather than the default choice.