I think that from the first post on you went further and further from Tosfos’ intent. Do you think a Kosher meat store has to look different than a Treifa meat store? If it would there would never be a case of Kavua. If you can’t tell then it’s Parush, if you can tell then you have no Shaila!
Tosafos is not saying that you have to be able to tell what makes it Assur and what makes it Muttar (i.e. To be able to tell that he is a Yid, or that the meat is Kosher). He is saying that the objects in question should still be Nikkar and not be seen as one big hodgepodge. In Gittin 64 Tosafos uses terms of Taaroves, which makes my point more clear.
In a group of ten people, each person is an individual. In the case of Mekadesh Isha Min Hashuk, the specific woman is Battul in the world at large. If you think about, this is actually how you would naturally look at it, whether you have the right words to describe it or not.
Chad Betrei is a soup, salad, pile, or a mixture, and is therefore Battul rather than being a Kavua. When it comes to people, a group is not soup.