For what it’s worth, this can happen with bridges too. It’s easier to express this situation on a separate way than using sidewalk=*, which only communicates the presence of a sidewalk but not whether it can be used.
One wrinkle is that emergency=* normally refers to emergency vehicles and personnel, typically police, firefighters, and paramedics. But these sidewalks are for anyone to use in an emergency. It’s sort of like the opposite of foot=destination. Presumably the law doesn’t prevent pedestrians from seeking safety while ignoring normal access restrictions, so access=no probably achieves the desired effect.