This covers uploading and downloading. But what about deleting?
I’ve tried accessing the file using these documented paths with a DELETE request (with curl) however I get a 404.
I think you must be right. GitLab believes strongly in iteration, so many features are released early and then more functionality is added to them. If you happen to be an early adopter of a feature, you may sometimes have to wait for new features to come in, or implement a workaround. If you upvote an issue that you would like to see implemented, that makes it more likely to be bumped up the priority list.