The question is whether children who are already in school are likely to develop an allergy due to lack of exposure at that point in their lives. If the answer is no, the only downside is parents having to make a different sandwich for lunch.

I'm allergic to peanuts and none of my schools banned peanuts. When I was in elementary school, another kid chased me around with a peanut butter sandwich for a couple of minutes before the teachers were able to stop them. I'm not saying this will happen to all kids, but the options for bullying get kinda scary when an everyday food can kill you. Kids at that age may not understand how serious allergies can be, so there's also the more mundane risk of a child with an allergy trying somebody else's food without knowing it contains allergens.

Later on in middle school there was a single peanut-free table, where kids were eating peanut butter sandwiches for lunch every day before I arrived. Fortunately they were willing to bring something else once I told them I actually needed the peanut-free table to be peanut-free.