To me it looks like the main issue is how to distinguish two different paths in OSM, not in real life. Whether we use a different main tag, or additional tag, or rely on existing sub-tags.
I think it would be simpler if we take two extremes and discuss how to separate them. Once we find a way that is satisfactory, we can discuss if the same can be applied to other cases.
Why don’t we take the first and the third photo from this post:
and try to devise a way to tell them apart? Hopefully it does not take a lot to explain the benefits of having them as different entities on a map.
Edit: I’ve created a wiki post for this: