Even if the airline complies with the request and does not issue peanuts, what is someone had their own bag and busts it out? Are they liable? I'm curious, it's a real question, I'm not trying to stir up anything.
Nowadays, there are so many foods that may not be overtly recognizable as peanuts but may have been processed in a plant that processes peanuts. What if someone opens up something which they don't even remotely suspect has been exposed to peanuts? Is the rest of the aircraft supposed to starve?
I mean, reasonable accommodation can and should be be made but if your child really has such a high sensitivity/intolerance, shouldn't you consider other means of travel, however impractical it may be?