Are “Positivity Rates” a Useful Statistic for an Epidemic

What are your opinions about the "positivity rate" statistic? As I understand it, positivity rate is defined as (Positive Tests)/(Total Tests) for some sampling period (day, week, etc). Since tests are: 1. not given to individuals on any basis other than a) showing up at a testing site voluntarily or b) possibly being given a test as a result of a physician's exam or hospitalization [note how different these two cases are]. and 2. results are grouped arbitrarily (sometimes by facility, sometimes by county, sometimes by city, etc., in other words, no consistent grouping) I fail to see that positivity rate is useful for any purpose. No control appears to be present at all. That is, there is little to prevent someone from being tested repeatedly day after day, or even several times per day, although honestly I believe that uncommon. Many factors can influence who is tested: day of week, holidays, special events, just got home from France, I'm off today and have nothing else to do, someone has a cough, someone else has a fever, my back hurts, etc. Using positivity rate as a reliable predictor of anything appears to be an abandonment of standard statistics and assumes that (in the case of daily sampling) each day's sample is representative of the whole population, a surely flawed assumption. While "positivity rate" is indeed easy to compute, are there not better methods available (e.g., random sampling of the population) that would provide truly useful information?