It can definitely hurt to be on the safe side.
The problem of false alarms can be crippling. In my day job I worry about things like antisubmarine warfare. The main problem is you have an enormous number of false alarms (whales, rocks, etc). You can't drop a lightweight torpedo on every contact because then you're out of torpedoes in a day or so. So you have to wait (often for an extended period) to classify the contact before you attack it. In the meantime, depending on where the contact is, it may sink one of your ships first. You have to balance those risks.
One of the most pernicious delusions is that human life is priceless. It most obviously isn't, or life insurance payouts would be infinite, and all cars smaller than a big SUV or Cadillac would be illegal, and the SUVs and Cadillacs would have $100,000 more in safety features. Various economic studies have been able to estimate the price of a human life.
The overall cost to society of the perhaps weeks of education lost to millions of children if policy was to close schools every time an area was in an SPC risk area is greater than the cost to society of a few dozen kids being killed. And that's anomalous, on AVERAGE you are probably seeing maybe 1-3 children killed/year by tornadoes in school.
And one could make the case that among those millions of hours of lost education are a few smart kids that could have gone on to medical school if they hadn't missed out on those hours of instruction, and found cures for diseases that kill thousands.
And of course has been probably already pointed out in many, if not most cases the children are safer in school than at home.
“The overall cost to society of the perhaps weeks of education lost to millions of children”
You’re kidding, right? This is government school we are talking about.