Question

You mentioned Professor Koppel’s explanation of the law of fixed status. You explained that in his view, the main distinction is between a concrete doubt, like a piece that became separated, and a theoretical doubt, where the question is what would happen if it were to separate. You raised two central questions about his view: 1. Why is this not true also in a majority that is not before us? 2. Why, when someone bought from the store, do we not treat it as a concrete doubt regarding that particular piece?
I understood his claim a bit differently. In my opinion, the main question is whether we are discussing only a single piece, or whether we are forced to discuss the entire set as a whole. Here, that indeed follows from the fact that the doubt does not relate to a defined piece. And that reminds me of the law of the two paths.

Basically, the law of fixed status is built on several assumptions.
1. I am forced to discuss the entire set, because there was no separation.
2. The prohibition definitely exists within the group (Koppel mentions this as a required condition for the law of fixed status. I think this is explicit in Rashi, though I am not sure it is required by the Talmud itself.)
3. There is no situation here of nullification.
The result is that we are forced to decide regarding the entire set, but that is not possible because of points 2 and 3.
This reminds me of the law of the two paths: if it is possible to discuss each one separately, then it is pure; but once we are forced to discuss the whole set, that is no longer possible, because it leads to a paradoxical ruling.
The question of why there is no law of fixed status in a majority that is not before us is not relevant, because condition 2 is not fulfilled there. The first question, why not discuss the piece separately, is still not so simple, and it still needs to be explained that we relate to the time when the doubt arose, as you mentioned.