As I said, BA and other airlines have strict liability and won't be interested in the finer details of level of risk. If told about an allergy, standard legally agreed procedures kick in.

I sense there's more to this than the actual frequency of event anyway - in about 300 flights over the past 3 or 4 years I can remember maybe 2-3 announcements, and it hasn't been a major issue to forgo the Frit. I like warmed nuts as much as the next guy, but it's not central to my in-flight experience. Most service animals don't cause issues, they're not Great Danes as a rule.

I'd speculate that this is more about feelings about loss of control over events, which underlies a lot of flyer psychology. It gets blown up in peoples' minds because it is yet another something external affecting their personal experience and further reducing their latitude to control what is happening to them, and maybe it feeds a "everything's going to the canine support animals" view of life.