Docker's build process does not provide the functionality to copy files out of an image without using an intermediate step. This would need something external to manage the build workflow with additional steps like docker cp as you suggested.
Rocker may be of interest which implements it's own build system via the Docker API with an extended set of Dockers build commands. A number of the useful features that users have requested and Docker refused to add have been added here.
Features includes MOUNTing volumes from the host during the build. EXPORT/IMPORT of files from a build. Multiple FROMs, one for the "build" container, and another for the "run" container.