From the scanning electron microscopy work here:
https://scienceofsharp.wordpress.com/2015/03/24/sharp-and-keen-part-2/
The very edge apex has to be around 0.1 to 0.05 micron in width to be shaving sharp. As of now, I do not believe it is possible to manufacture a carburized layer that is not only that thin but also exactly centered such that your theoretical knife would be always self-sharpening.
https://scienceofsharp.wordpress.com/2015/03/24/sharp-and-keen-part-2/
The very edge apex has to be around 0.1 to 0.05 micron in width to be shaving sharp. As of now, I do not believe it is possible to manufacture a carburized layer that is not only that thin but also exactly centered such that your theoretical knife would be always self-sharpening.