Not to throw a wrench into a thread that's dying anyway but I wanted to point out that even Mastro Livi says a hanging strop will round and kill an edge. He also wont use leather because it "has flakes" and makes the edge rough to the face. The strop his father developed has a type of "Skin" but he says it's not leather. This is the Livi Loom strop. He also doesn't use linen at all because he says it makes the edge harsh.

So this type of thought is shared by personal experiences, although not considered the norm, by guys that know their craft.

To me , stropping is part of the fun and I like doing it. But everyone has their own experiences.