AFAIK people with egg white allergy also have to avoid cooked foods.

My understanding (not a chemist nor doctor) is that it's specific bits of the protein that trigger the allergic reaction, so eve if the whole protein breaks down parts of it will survive and will cause trouble.

I suppose this is similar to how we use broken down bits of virus to trigger immune reactions with vaccines.

And what about people who eat actual raw egg? I routinely eat freshly-made cake batter (made with raw eggs; I just clean the bowl, I don't actually gobble tons of raw cake batter), for instance. It's perfectly safe because I live in a country where they actually check eggs for salmonella before selling them and people routinely eat raw eggs on top of things.