It's an interesting point. I would say that the edge is soft like cheese before and after using it, hence why everyone would agree that delicate handling is good practise. The general view of using a linen strop before leather is to warm the edge and make it malleable so that when stropped on the leather, it's more pliable and the edge should re-align with less effort. So in the case of stropping after a shave, softer is by consensus, desirable? This is my view, but respect that others have their preferences

I personally like to strop after shaving and before because I like stropping and I have had no problems to my edges...