I suspect wood will always dull the blade.
I've built a lot of architectural models using soft woods like balsa and bass, they most certainly do dull blades, but I'm cutting not trying to sharpen them on the flat side.
I'm going to have to research this to validate, but my current theory is that the coefficient of friction on a leather strap, and the way it conducts or absorbs heat is different than that of wood.
That the friction and heat are in such short time periods that your senses don't pick up on it don't mean that they are not there.
Sort of like a needle running through the groves in a vinyl record. The friction and heat melting the vinyl for a micro-second thereby insuring each time you play the record it will sound every so slightly different and eventually wear out. Your senses simply cannot pick up on this.
One could conduct an experiment flat side rubbing a knife on leather and then wood to see which material transfers heat into the knife or transfers the heat into the the wood or leather.
Can I change my answer? I just found this:
Razor strop
https://en.wikipedia.org/wiki/Razor_strop
Quote:
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A razor strop (or razor strap) is a flexible strip of leather, canvas, denim fabric, balsa wood, or other soft material, used to straighten and polish the blade of a straight razor, a knife, or a woodworking tool like a chisel. In many cases stropping re-aligns parts of the blade edge that have been bent out of alignment. In other cases, especially when abrasive polishing compound is used, stropping may remove a small amount of metal. Stropping can also burnish (i.e. push metal around on) the blade.[1]
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Sounds like a soft wood will indeed sharpen a knife.
That is my answer, but I could change my mind a couple of more times.
