I think you're missing my point.
If you never shot a JPEG, and only shot RAW files on both cards in your camera, you would still have a complete RAW file and a JPEG, because the JPEG is embedded in the RAW file's metadata.
What you see when you look at your RAW file in something like Bridge, or your OS preview (Windows Explorer or Mac Finder) is not the RAW file because the RAW file is not an image. You are looking at the JPEG preview of the RAW, which is the same as the other JPEG that you saved separately.
That's why I say it seems to be unnecessary to have two JPEGs.
Here is a screenshot of a RAW folder in Bridge. All these are Nikon RAW (.nef) files. You can see that the thumbnails here are fully processed JPEGs and I can click one and get a full size preview, then cycle through them and mark them for saving or deleting, add keywords, etc. The RAW file is never touched, and if I open that file in Adobe Camera Raw, it will be the RAW file, not the JPEG that opens. I can edit and save the result in any format, and there are no extra JPEGS to delete.