We are talking about a 4-sided paddle, right?
It appears to me that they would probably just use the Coticule part restoring bevel flatness, when the cushioned pasted strops stopped working because the edge became too convex after a prolonged time of use.
I don't think they intended the Coticule to be the finishing side of this honing tool.
Quite frankly, I believe Coticules in general were often more used for "bevel-setting" than for finishing, in the old days.
The traditional method is to use the stone with a "sharpening lather" (what we now call "slurry", and has, besides the resemblance, nothing to do with "shaving lather"), till the faces of the bevel are flat and the edge is nice and smooth. After that further refining is done on the pasted sides. The edge is stropped on clean leather daily and maintained with a few swipes on the finest paste at the earliest signs of deterioration.
All this doesn't mean the stone would not be able to deliver a great finish, just that it wasn't put there to do that. That Coticule became looked at as mere "finishing stones" is fairly recent development that sprouted on the US based internet forums. Probably because Coticule, when used with water have little trouble "improving" the edge left by a Norton 4K/8K, which has been the most recommended stone for sharpening razors, at least for the recent years of straight razor revival. If Coticules came after the Norton, they
had to be finishers, right?
The truth is slightly more complicated than that, I'm afraid.
A quick Unicot will give you a good idea of the actual finishing capabilities of this one.
Kind regards,
Bart.