When on less than predicted fuel reserve plus 16hr duty plus high workload environment, there is little time to nuance discussions with ATC. "Mayday Fuel" is a lot easier, get to land ASAP. Fill out the paperwork later. Low fuel = emergency. Sounds fair to me.
It’s not quite as simple as that. Firstly minimum fuel is not emergency fuel. He’s had quite a long flight, with 16 hours of looking at the projections, so unless something outside the aircraft has changed, there should be a valid fuel plan. If nothing changed at Sydney, then there is no excuse for not having gone to Brisbane.
His plan should always have included the minimum fuel (which is inviolate), fuel for an approach, 110% of the fuel required to get from any point to the start of the approach, nominated ATC holding fuel, and any weather holding fuel.
By declaring an emergency, he immediately goes to the top of the queue. But what if ATC wanted 30 minutes of hold, and he only had 20? He’s still min fuel, but unless he actually holds beyond his available holding fuel, he’s not in an emergency.
My guess would be that ATC had 10 or 20 minutes of hold on the plan, but then they decided to ramp it up to more than that. Unless you’re told well down the track, that will immediately cause problems.
QF12 was a little behind and had to hold a couple of circuits at about the same position as UA839 when they declared the emergency.
They had the fuel to do so, but United didn’t. QF’s plans are very much minimum plans, so I’d love to see the United one.