The Topaz product looks interesting. Thanks for the link.
They ask: Can you tell the difference vs. the original RAW? (https://topazlabs.com/static/jpeg-to-raw-ai/img/compression-bna.png )
Answer: Yes, very easily. The right-hand image has detail around the edge of the mushroom that is absent in the middle image. I assume those are the raw image (converted to sRGB) and the “improved jpeg” respectively.
Some of that detail has been removed in the jpeg image, and some detail is swamped by jpeg artifacts. Fixing the artifacts has also removed some detail.
Expanding a small gamut to a larger gamut, eg sRGB to ProPhotoRGB, is trivial. But doing it accurately is difficult. It assumes we know what process shrunk the gamut, and that it is reversible. I doubt that either assumption is true. For example, the jpeg may have had local adjustment of saturation (like local adjustment of tones), and reversing that accurately is difficult.
I can certainly believe we can start with a horrible jpeg that can’t be edited, and process that image to remove artifacts and invent tones, colours and detail so that we can then edit the image. The result may be pretty, and may be credible.
But will it be as accurate as a process that starts from raw instead of a jpeg? No, because data has been lost.