I'm not 100% sure HKG is not nominally profitable as of right now but here is the evidence I use to assert my statement that it is not significantly profitable. Break even, perhaps. But I'm sure we would hear about it with great fanfare once there is a meaningful profit being made. I have flown AA metal to HKG 3 times now and each time I paid less than $800 USD. 5 of 6 times I have cleared into J.
I think there can be an overemphasis on the profitability of Long-haul international for the large US carriers. While none of them can fly a route that bleeds money for obvious reason (well at least they shouldn't, but airlines may do stupid things sometimes) As long as they are somewhat profitable they serve their purpose allowing access to everywhere they need to go. Sure alliances help and JVs more so, but the true value of the routes, especially for paid premium demand, has to be what contributing factor does it make that allows the airline to be selected for most of that pax/corporate travel.
As an anecdote, I'm based in CRW, on an annualized basis we have almost the exact same capacity for the merged AA and HKG does with a single 77W daily. I can't argue that CRW is as important of a city as HKG (we only have 50k people here), yet currently similar capacity. The value of the long-haul routes does go beyond just the direct earnings of the route sometimes.
And since we can't get from CRW-DFW in time to catch HKG the same day, we really need an Envoy e175 to restart that route with twice per day service next year!