My guess is that it is unlikely to see your request for a more generalized script or Dockerfile runner realized because that (Dockerfiles) was the original implementation of Actions during the beta; they pivoted away from that to the current form.
I tend to stick with bare scripts and npm scripts as much as possible though, so the environment doesn't matter as much.
The concept of actions is new, but it is brilliant compared to traditional approach of doing everything inside the CI jobs, or bring your own docker images.