Miller was narrowed to the provisions of a sawed-off shotgun/militia argument and opened the door to regulation of machine guns, silencers, et al, wholly to control gangster activity when there was not enough law-enforcement to do the job.
That's not really true. Obviously, machine guns and most of the items covered under NFA 34 ARE the types of arms useful to a militia. The Miller decision was simply ignored, not broadened, to include such arms.