Simplified is good, and correct. Of course, the gasket under the copper disc will fail almost immediately. Same for the nylon valve seat.
Pesky
All the non-metallic components will degrade at relatively lower temperatures, but they do not provide a flow path large enough for quick depressurization. A leaky gasket will not be sufficient in an intense fire.
Simplified calculations implies an approximation... that it is correct, well I have made mistakes in the past and I will guarantee you I will make some in the future. I just hope to catch before anyone else does.