You can find really exceptionally fine examples. I think sebastian has one as fine as mine was. I mean, mine was pretty damn fine before I wrung everything out of it. There are some that are prefinisher/finisher fine.
I've tried Sebastian's as pictured above, and it seemed very similar to my "genre Levant--lisse" as shown. Don't know if he has another one, although knowing him, he probably has a shoe box full of them. ;-) That one, which is in France still, had been smoothed by quite a few blades. I'm going to try to smooth one of these I've got here kind of like how you said and see what happens.
The other thing about the company at Saurat is that they do not sell outside of EU addresses. Maybe it has to do with receiving funding from the French government (by whom they are supported); so one has to deal with smaller merchants who will sell them to the US address. That may be why they are not so well known here, and I do wonder about their former prevalence here as well. Mine have been purchased in France, where they are extremely easy to come by (i.e., a local hardware store in my wife's small home town in the Vosges mountains has them); but even there, I don't think that their maximum potential, if it is indeed as high as suggested, is recognized.
Likewise, the stone calle Levant, of gray color and sold in all standard dimensions, delivers two varieties of whetstones and a third variety, custom made under the name "Levant hone for pruning shears"