I've been vegetarian/vegan for 17 years which, thankfully, means that my dietary restrictions are by choice and not because of a life-threatening allergy. But, what I've learned over the past 17 years is that people have no clue what's in the food they're eating, how to read labels, or how to properly accommodate dietary restrictions. I can't tell you how many times someone has offered me something claiming it was "safe" when it wasn't. Many people seem to only recognize the offending ingredient when it's in it's most obvious form, i.e. "I can't see any meat or cheese, therefore it must be vegan." There is no way I would trust 150+ strangers to keep me safe from deadly allergens, and that's assuming they all heard, understood, agreed, and remembered to comply with the announcement in the first place.
Ever notice how many food labels say "This was manufactured in a facility that also processes..." or "May contain trace amounts of..." Those production lines are cleaned and sanitized in accordance to food safety standards when switching from one product to the next and yet, the companies are so concerned that somewhere an allergen particle has become trapped in the groove of a screw on the conveyor belt which will end up contaminating the next product that rolls by and kill someone, that they won't risk the liability of claiming their food is 100% safe, so they put that disclaimer on the label. They don't want the liability. And, I imagine, that's where the airlines will end up. They can't guarantee every passenger will comply, that every surface is free of peanut residue, or that every air duct is clear of particles, so they won't even try to assume that liability. Flying will become "at your own risk."
ETA: If you are deathly allergic to cats, just don't come to my house. I'll meet you at Starbucks. I could drop my five cats at a friend's house, spend the week prior to your visit wiping down the walls, scrubbing the floors, cleaning all the surfaces, laundering all the fabrics, vacuuming the vents, changing the air filters, and putting on brand new articles of clothing straight out of the bag just before you arrived, but I still wouldn't be confident that there wasn't cat dander lingering somewhere. It's just impossible to make those assurances. I doubt an airplane would get one tenth that level of cleaning between flights.