Seems like in the context of this use case, the medical community would adopt the tests with the higher specificity, and there would be market pressure to lower the cost, if needed. Seems a bit of a reach to point to tests used for use case A to discount use case B.

Yes, it is possible to accurately detect antibodies with certain antibody tests (primarily, blood draws) administered by certain parties. But now you have a complex patchwork of antibody test exception standards formulated and enforced to satisfy the preferences of a small number of individuals, most of whom simply object to vaccination on ideological grounds. These folks should just get vaccinated.