Let's take your analogy of a car accident further, NiceGuy. You state that, if your child was killed by a car, you wouldn't want all cars banned. I accept that. But wouldn't you be looking at the factors involved, to see if it was possible to reduce the risk of a similar accident happening to another child?
For example, if speed had been a factor, you might consider campaigning for speed bumps, or a proper pedestrian crossing to allow children to cross a fast road safely, or maybe for a lower speed limit - ie 20mph in an area where there are lots of children around - near a school, perhaps.
Or if some particular aspect of vehicle design had made the accident worse, or had contributed to it's happening in the first place, you might want that particular design feature modified, if you felt it would be a risk to other children.
It is widely accepted that it is a bad idea to drive under the influence of alchohol, as this can lead to tragedy. Presumeably the drink-driving laws came about because people saw alchohol as a factor in road deaths/accidents, and thought it was a good idea to try to reduce one potential contributory factor.
Making it illegal to drive drunk, or putting speed restrictions in place, or building a new pedestrian crossing will not stop ALL road deaths, but it will stop some happening - and that is surely a good thing.
In the same way, banning nuts in school will reduce the risk factor for nut allergic children - it won't stop all allergic reactions, and it won't change the risk factors outside school, but it will help a bit - and I can see how someone with a nut-allergic child would think that was a good idea.