The most accurate approach would be to do repeated blood tests of a large nationwide study population looking at both antibodies and memory T cells. The CDC really should have been doing that nationwide for the past year.
The Red Cross Blood Donation centers perhaps come closest to doing this. From their emails, it sounded like they never saw widespread active antibodies (until a few months ago).
The Red Cross only did antibody testing which has a significant false negative rate, especially on patients who recovered from mild infections many months ago. That's why getting accurate numbers would require repeatedly testing the same subjects at regular intervals, and also assaying their memory T cells.
How can you do that with over 50% of the population fully vaccinated?
The point is that they should have been doing that since tests were first available, before anyone was vaccinated. Even now it would still be a useful study in the unvaccinated population.