I can't say I know much about Concorde. Did it use fuel for Mach trim? Obviously, there are ways to get more precise, but unless you're using fuel for something more critical than just running the engines, most folks don't go to the trouble.
That said, I haven't worked on an airliner. Perhaps the customers demand more than the minimum since they're so obsessed with carrying just enough fuel to get there. But, on the military and GA side of the house, no one seems to care much if your weight calculations are a few percent off. That's why we weigh the actual aircraft before and after each flight when doing performance tests. The answers are highly weight dependent and the fuel system can't be trusted.