As someone with past involvement in procedure design and risk management, though not in aviation, I am surprised at the order of the early items in this list. I would expect fuel cut off to appear early, certainly before setting the parking brake. In the G-VIIO case the residual momentum and the dying thrust from the operating engine could probably have moved the aircraft clear of the pool of burning fuel.
Valid considerations, but one must consider the cause effect of specific annunciations in order to design for a desired response.. What you assume is correct but statistical experience must be also considered "Pool" fires are thankfully rarities as a cause for the initial annunciations to the crew. Thus the expected response from the crew is reflected in the current procedures.
The issue in my mind is how to annunciate to the crew in a timely fashion that a pool fire has occurred and that appropriate reaction is expected.