Dockerfiles are a mostly adequate prototyping tool but are not great for generating production builds. Lack of modularity, cascading versioning / dependency management, reproducible builds, ... every time I've used Dockerfiles in anger I've cobbled together another 60% of a build system out of bash scripts.
I wish Dockerfiles would just fade away into the background, and be replaced by something more similar to an archiver but with better integration with repositories and versioning metadata.
There are some people trying to build alternative toolchains for Docker builds that remove Dockerfiles altogether, e.g. https://buildpacks.io/ and (in a very different approach) Nix-based builds.
My personal approach for Python applications' Docker packaging (https://pythonspeed.com/products/pythoncontainer/) was similar to yours: wrap the build process in a script. I wrote it in Python rather than bash, so it's more maintainable, but a Ruby shop might want to write theirs in Ruby, etc..
I wish Dockerfiles would just fade away into the background, and be replaced by something more similar to an archiver but with better integration with repositories and versioning metadata.