Note 2.— .... . It should be noted that Pilots should not expect any form of priority handling as a result of a “MINIMUM FUEL” declaration. . .....
Typical bureaucratic response.
Why would you bother to call "minimum fuel" if it is not going to reduce flight time to landing.
the pilot calculates that any change to the existing clearance to that aerodrome may result in landing with less than planned final reserve fuel.
When being vectored, how does a pilot know what his landing time will be. An extra minute on a downwind leg could be the difference between a "minimum call" at 150 miles and a "mayday" call on base.
There does not appear any requirement on ATC to give a landing time in reply to a minimum fuel call.