Yeh it's all a bit annoying, I wonder how many nuts incidents actually caused medical emergencies onboard last year.
I was on a "no nuts" flight a couple of months ago. Due to BOB, i had brought some Graze nuts to feed my hunger on the 3.5 hour flight and wasn't able to eat them. At one point the crew said the passenger was having a flare up and please could everyone double check that no-one had opened any peanuts.
I'm pretty sure the flare up would be due to all the nuts bed into the dirty economy seat lining and nothing to do with any of the other passengers. I believe BA could make allergy sufferers (of all ilks) more comfortable by serving a few more pretzels and deep cleaning more often. The "don't eat nuts" thing, it's about as useful as "please take care on the stairs" and feels very legal/compliant as opposed to beneficial.