False negatives are surely far more concerning. That means there are people wandering around, mixing and often in close contact for lengthy periods of time, who are actually covid positive.
One child missing the odd day whilst getting a false positive sorted inconveniences that one child and their household.
A false positive can end up with greater transmission, most people affected, the eventual closure of a bubble, and the risk of a vulnerable member of staff/pupil or their family may then catch it.