The open bonnet is to expose the spring to air so it is kept cool and therefore has the correct force downwards on the seat. If you specify a closed-bonnet PSV (like the vast majority of PSVs) for steam service then the whole valve body can get up to the steam temperature, including the spring, and it doesn't lift until a much higher pressure than your bench test indicates.
Quite remarkable that they found someone to help them on this 5-second bit of animation who had experience with using steam in an industrial process plant or boiler, and not just a domestic plumber.