Eh not really, these aren’t measurements these are for the most part binary tests the current assays seem to trigger on AB’s for multiple coronavirus strains and even worse other common viruses.

Without knowing the specificity and sensitivity of this specific test you can’t say any “inaccurate guesses” based on it is an upgrade.

Say the test has really poor sensitivity but 100% specificity then sure it might not identify a lot of past infections but it won’t produce false positives so which ever figures come out you can extrapolate of them fairly easily.

If it has terrible specificity then it’s a whole other problem unless you have additional tests that have high specificity that you can use to exclude false positives.

But if you want to know "what percentage of my population have had coronavirus in each town and age group", then these tests, combined with research to find out the sensitivity and selectivity, will answer that question.

Most of the big decisions governments have to make depend on only aggregate statistics after all...

AB testing yes, this specific test maybe which is why the GP was asking about the assay.

The current AB tests were found to be insufficient.