Actually, I have lived in multiple places in the US and many schools do not have a theater as you describe although most have some kind of elevated “stage” somewhere in the school for presentations and assemblies. Sometimes this is in a “multi-purpose” room that serves as a gym, a cafeteria and an assembly place—but does not always have a curtain.
Not all schools do theater/plays, either. That stage is used for many other things—so its existence is not tied to theater activities.