Becca the majority of children with allergy to milk and egg actually outgrow it by the time they reach school age. Nut allergy is outgrown by a far lesser per cent and in some is an indefinite and potentially life threatening allergy.

As mentioned above they also present a choking hazard in young children.

Allergies are taken seriously nowadays. As is needless infant death. The risk they present is small but easily eliminated and therefore it is eliminated. That makes perfect sense to most parents of young children. Especially those coping with allergies.

Schools are not the only place to take the sensible approach and ban something that doesn't need to be there, but has inherent risks for a minority of children. Airlines (some) have also banned nuts on board. Adults/children can have severe reactions just by being in close proximity to someone else eating them.

Would you rather your flight unexpectedly forced to land mid flight to off load a dangerously ill passenger just so someone else can eat nuts? The airlines thankfully obviously recognise the risk.

You ask if schools should ban lunch? I think it is a lot easier to ban the foods that have proven risks. I take it you are neither a parent of young children or a relative of someone with a nut allergy.