It's not the book-keeping that's the issue, it's the physical determination of status. For antibody status, you have to do an antibody test, which is strictly

It's not the book-keeping that's the issue, it's the physical determination of status. For antibody status, you have to do an antibody test, which is strictly more complex/expensive than a COVID vaccine (it took 3 days when I got it done), so it's not viable at population scale. It's similar to the reason that monoclonal antibody therapy is not a scalable treatment for COVID infection - better to minimize the chance of needing such treatment by just getting vaccinated.