Assume probability of false positive is 1%. If you are tested weekly, there is a 41% chance you'll falsely test positive at least once in a year. If you are tested every workday, 93% chance. This is assuming there is no malfeasance.
If you assume a false positive probability of 5%, the probabilities go up to 93% and 100%.
The negative effects of false positives are the same whether kids are using soda or something else is causing them. At some point, the costs have to be weighed against the benefits.
Here is a false positive/false negative simulator I put together last year (thrice silently banned -- so I stopped trying to do more after restoring it one last time) helps you explore what happens with various scenarios of infection rates and false positive/negative probabilities.
Linking to the discussion to provide context for the app:
https://www.covid2020.icu/false-positive-false-negative-simu...