I suppose. But that's impractical in situations when flights only run a couple of times a week. And what happens if you end up with the dog on a connecting flight? You'd be unaware of it until you got to the gate - all your checked bags and everything would already be in transit. And if the person requiring the dog got advanced boarding, you may not even realise there's a dog on board. Would the airline then be liable if you had an allergic reaction and they didn't explicitly inform you that there was a dog in the cabin?

*shrug* the practicalities of it all just interest me.